The　Melnikov　method　is　extended　to　a　class　of　hybrid　piecewise-smooth　systems　with　impulsive　effect　and　noise　excitation　when　an　unperturbed　system　is　a　piecewise　Hamiltonian　system　with　a　homoclinic　orbit.　The　homoclinic　orbit　continuously　crosses　the　first　switching　manifold　and　transversally　jumps　across　the　second　switching　manifold　by　the　impulsive　effect.　The　trajectory　of　the　corresponding　perturbed　system　crosses　the　first　switching　manifold　by　applying　the　reset　map　describing　the　impact　rule　instantaneously.　Then,　the　random　Melnikov　process　of　such　systems　is　derived　and　the　criteria　for　the　onset　of　chaos　with　or　without　noise　excitation　are　established.　In　addition,　the　complicated　dynamics　of　concrete　piecewise-smooth　systems　with　or　without　noise　excitation　under　the　reset　maps,　impulsive　effect,　and　non-autonomous　periodic　and　damping　perturbations　are　investigated　by　this　extended　method　and　numerical　simulations.