  We investigate the crossover behavior between special and ordinary surface
transitions in three-dimensional semi-infinite Ising-like systems with random
quenched bulk disorder. We calculate the surface crossover critical exponent
$\Phi$, the critical exponents of the layer, $\alpha_{1}$, and local specific
heats, $\alpha_{11}$, by applying the field theoretic approach directly in
three spatial dimensions ($d=3$) up to the two-loop approximation. The
numerical estimates of the resulting two-loop series expansions for the surface
critical exponents are computed by means of Pad\'e and Pad\'e-Borel resummation
techniques. We find that $\Phi$, $\alpha_{1}$, $\alpha_{11}$ obtained in the
present paper are different from their counterparts of pure Ising systems. The
obtained results confirm that in a system with random quenched bulk disorder
the plane boundary is characterized by a new set of critical exponents.
