  In this paper we treat the numerical approximation of the two-phase parabolic
obstacle-like problem: \[\Delta u
-u_t=\lambda^+\cdot\chi_{\{u>0\}}-\lambda^-\cdot\chi_{\{u<0\}},\quad (t,x)\in
(0,T)\times\Omega,\] where $T < \infty, \lambda^+ ,\lambda^- > 0$ are Lipschitz
continuous functions, and $\Omega\subset\mathbb{R}^n$ is a bounded domain. We
introduce a certain variational form, which allows us to define a notion of
viscosity solution. We use defined viscosity solutions framework to apply
Barles-Souganidis theory. The numerical projected Gauss-Seidel method is
constructed. Although the paper is devoted to the parabolic version of the
two-phase obstacle-like problem, we prove convergence of the discretized scheme
to the unique viscosity solution for both two-phase parabolic obstacle-like and
standard two-phase membrane problem. Numerical simulations are also presented.
