​​Yes, blister packs are recyclable (for example with machines like this one ) but chances are there's no recycling company in your area that will accept and recycle it unless you are able to separate the different materials yourself.
Blister packs like the one you posted typically consist of plastic (usually PET or PVC) and aluminium.
The problem with composite waste materials is that they are more difficult and costly to recycle compared to homogeneous materials, because you need to separate the different materials.
Additionally plastic-aluminium composites only form a relatively small-volume waste stream, which makes it difficult to make the recycling process economical.
Recycling companies that recycle blister packs do exist, for example this US and UK-based recycler
but I think that's one of the few
and it seems you actually have to pay them to get it recycled
(you have to buy a waste collection box and send it back once it's full).
In general it's always best to ask your local recycling company whether they recycle a particular product, and what the appropriate way of disposal is.
That's because different recycling companies make different choices as to which types of waste they process and how exactly they collect and process it.
If your local recycling company doesn't recycle it you could try and find another company a bit further away, but if you do find a suitable recycler keep in mind that moving trash around may cause more environmental damage than you gain from recycling.
BTW when inquiring about the recyclability of a particular material, always check the recycler's definition of 'recyclable'.
Many recyclers will say they do 'thermal recycling' which means it will be incinerated.
sustainability.stackexchange.com/users/99/THelper
There are blister packs which appear to be made entirely from aluminium
and I put these in the recycle bin in their entirety.
I have also been recycling the blister packs made from plastic and aluminium.
I do this by occasionally separating the aluminium from the plastic in a sort of game of 'patients' by trying to separate as much of the aluminium from the plastic as possible.
With some blister packs, eg asprin, it is possible to achieve 100% and most others around 60 to 90%.
However, with some, especially where the blisters are very small, I give up after a few seconds if I am struggling however I have occasionally achieved 100%.
Needless to say the aluminium gets recycled and the remaining pack has been discarded.
I can while away an hour or so on this when I have things I need to think over quietly or I have little else to do.
Far better than this would be a National/International campaign to have all blister packs made entirely out of aluminium; it is done by some and can surely be done for all medicines.
sustainability.stackexchange.com/users/5870/John H Payne
Only thermo plastics have a recycle value, thermoset plastics do not.
Even the thermo plastics are limited as recyclate - grade 1 recyclate, by grade 2
the polymers strands will no longer bond and the resultant product will develop weaknesses and start to split.
As stated in the first answer, 'Yes... ...need to separate the different materials' it is this which poses one of the biggest problems in recycling plastics, it's best done at source (at home if you like) as the cost of doing it on mass is high.
Hope
this helps and enlightens.
sustainability.stackexchange.com/users/4800/Andy
I've experimented with soaking foil-backed blister packs in caustic soda solution, commonly sold as a material to unclog drains.
Caustic soda (sodium hydroxide, NaOH) dissolves the aluminium foil.
The caustic soda solution can burn skin, so it needs care in using it.
The dissolved aluminium produces sodium aluminate solution which can be flushed away with lots of water.
The blister pack plastic is usually PET which can be recycled, and the foil is usually bonded to the blister tray with LDPE film, which also remains after the aluminium is dissolved, and which can be combined with other LDPE for recycling.
When I was 11 or 12 years old, I used to work at a dispensing pharmacy after school.
My tasks consisted of delivering prescriptions to the recipients by bicycle(!) and literally washing the returned glass bottles that the customers brought back, soaking the labels off them, washing, rinsing and air-drying the bottles.
Simpler times fifty years ago in a smallish New Zealand city.
sustainability.stackexchange.com/users/6923/murray
In my household unfortunately we must take a number of tablets daily on permanent repeat prescriptions, mainly from plastic/aluminium bubble packs.
But some are supplied in totally aluminium packs, which are readily re-cyclable.
So there is an alternative - which is for drug manufacturers to be forced by law to use only single-material packaging.
If some can, why not the rest?
sustainability.stackexchange.com/users/5379/pete locke
Now, in management of recurring everyday waste, this is something totally unavoidable.   Are tablet strips (what they call blister pack strips), after use, recyclable? Can they be dumped with dry waste along with other plastic such as polythene covers?   I have been collecting them for over a month now, with the hope that there must be a responsible way to dispose of them.
Are used "blister packs" recyclable?
sustainability.stackexchange.com
<recycling><waste><packaging><waste-minimisation>
sustainability.stackexchange.com/questions/6108
sustainability.stackexchange.com/users/2734/Whirl Mind
Blister packs are recyclable but the component parts,  including PET plastics and LPDE film, may need to be separated for recycling. Some blister packs are aluminium and readily recyclable. It is best to ask your local recycling company how to dispose of blister packs. PET and aluminium blister packs are recyclable, though you should first check with your local recycling company.
Blister packs are recyclable but you should check with your local recycling company. PET and aluminium packs are recyclable.