the stage let $\Sigma \subset \mathbb{R}^3$ be a closed, bounded, and sufficiently smooth surface which splits $\mathbb{R}^3$ into a bounded domain $\Omega_+$ and an unbounded domain $\Omega_-$, and let $\nu$ be the unit normal vector field at $\Sigma$ pointing outwards $\Omega_+$. Our goal is to study Dirac operators acting in $L^2(\mathbb{R}^3)^4$ which are formally given by $$\label{def_A_eta_formal}
  A_{\eta, \tau} = -i c \sum_{j=1}^3 \alpha_j \partial_j + m c^2 \beta + (\eta I_4 + \tau \beta) \delta_\Sigma,$$ where $m$ is the mass of the particle, $c$ is the speed of light, $\alpha_1, \alpha_2, \alpha_3, \beta \in \mathbb{C}^{4 \times 4}$ are the Dirac matrices defined in below, $I_4 \in \mathbb{C}^{4 \times 4}$ is the identity matrix, $\eta, \tau \in \mathbb{R}$ are the interaction strengths, and the $\delta$-distribution acts in a symmetric way as $$\delta_\Sigma f = \frac{1}{2} (f_+|_\Sigma + f_-|_\Sigma), \qquad f_\pm = f \upharpoonright \Omega_\pm.$$ In order to introduce $A_{\eta, \tau}$ in a mathematically rigorous form as a self-adjoint operator in $L^2(\mathbb{R}^3)^4$ we require that functions in the domain of $A_{\eta, \tau}$ satisfy suitable coupling conditions on $\Sigma$. To find them, we note first that the distribution $A_{\eta, \tau} f$ acts on a test function $\varphi \in C_0^\infty(\mathbb{R}^3)^4$ as $$\langle A_{\eta, 