Requirements for travel between Mexico and the US are covered by the " Western Hemisphere Travel Initiative ".
That website states in part that : U.S. citizens and citizens of Canada, and Bermuda traveling by air between the U.S. and Canada, Mexico, Central and South America, the Caribbean, and Bermuda are required to present a valid passport or other WHTI-compliant documentation to enter (or depart) the U.S One of the "other WHTI-compliant documentation" items listed is a US Permanent Resident Card (Form I-551) - or a Green Card - which you have stated you do have.
So as far as leaving and returning to the US by air, you are covered without a passport.
In general Mexico also accept a US Green Card for entry, although I'm not certain that this also applies for Mexico citizens.
However even if it does not, then your Mexican Voter's Card IS acceptable for entry, presuming it has a photo on it.
The only thing I'm not sure about is departing Mexico back to the US.
I believe that your Green Card will also be sufficient there
(it certainly would be if you were not a Mexico citizen),
however I am not 100% sure of that for Mexican Citizens.
travel.stackexchange.com/users/984/Doc
The general consensus on several travel sites like Open Travel , Answers.com for people in your situation is that you need a passport to fly.
A Mexican consulate can issue you a new passport or an emergency travel document if you cannot get your passport in time.
There are options other then flying where passport is not required for entry, such as driving or arriving by sea.
CORRECTION
As per Star Alliance guidelines it is possible to travel with Mexican Voter ID card as a passport exemption
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You can also use your mexican military ID card (the card when you turn 18 you must get) if it has a photo with it.
I know it can be used for land travel
but I am not sure if they take it for air travel.
When we crossed into Mexico last year at the border they stressed to get a mexican passport soon.
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In March 2016, I flew out of Aguascalientes to Houston, TX, and I am both and American and Mexican.
I did not have my Mexican passport, and that presented a problem of "overstaying" my "visa" as an American.
It's impossible; I know; however, that's what happened.
A lawyer had to write a document that stated that I was in violation of Mexican law, and this time I could leave without penalty or fines; however, the next time ... .
You are required to have a Mexican passport to leave Mexico by air toward the United States.
An INE will not suffice.
travel.stackexchange.com/users/52595/Tom
As stated in Timatic , the database used by airlines, the following Mexican documents are accepted in lieu of passports: national ID card certified copy of birth certificate consular registration certificate of Mexican nationality naturalization letter Matricula Consular Constancia de Identificacion voter's certificate with photo.
And for returning to the US, your green card is enough
So no, you do not need a passport.
travel.stackexchange.com/users/39782/Crazydre
I'm Mexican and a US Permanent Resident.  I'm going to fly into Mexico from the United States, and I want to know if I can use my Mexican voter's card to check in at the airport, or will I need my Mexican passport?  I'm asking because I don't have a Mexican passport, and I will need to apply for one, but it would be much easier if I could just use my Mexican voter's card.
Is a Mexican passport needed to fly into Mexico from the United States?
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<customs-and-immigration><mexico><us-residents><mexican-citizens>
travel.stackexchange.com/questions/23290
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As stated in  Timatic , the database used by airlines, the following Mexican documents are accepted in lieu of passports: national ID card, certified copy of birth certificate, consular registration, certificate of Mexican nationality, naturalization letter, Matricula Consular, Constancia de Identificacion, or voter's certificate with photo. You can also use your mexican military ID card if it has a photo with it. A US Green Card will be sufficient for leaving and returning to the US, and may be acceptable for entering Mexico. Although there is some debate, it would appear a passport is not required for travelling between the US and Mexico. Other documents, including Green Card, Mexican national ID card, etc. are accepted at immigration.
You need a Mexican passport to leave Mexico for the US and you cannot use your INE. Both the US and Mexico accept documents other than passports for travelling between the US and Mexico. These documents include Green Card for returning to US and national ID card and certified birth certificate, among others, for Mexico.