  We consider the obstacle problem with two irregular reflecting barriers for
the Cauchy-Dirichlet problem for semilinear parabolic equations with measure
data. We prove the existence and uniqueness of renormalized solutions of the
problem and well as results on approximation of the solutions by the
penaliztion method. In the proofs we use probabilistic methods of the theory of
Markov processes and the theory of backward stochastic differential equations.
