Good question, I'm going to take that statement "All of their strengths, none of their weaknesses" as literally just that and assume he can be shot multiple times and survive and can regenerate just like them. When he's locked in that chamber and those large metal pins puncture his body they look rather large and numerous. I think the reason why he doesn't take a massive amount of damage is that he relies on his serum to survive instead of blood. I imagine blood is integral for him to regenerate and heal quickly so my assumptions are that they never put him into too many compromising situations where he would require large amounts of blood.
The only times this was the case was at the end of both films and after he drinks the blood he becomes noticeably stronger and his wounds healed.