Does anybody know how to get Bloodrayne to accept BOTH mouse AND joystick AT THE SAME TIME?

I'm afraid there is no way to do it. Everything is stored in the System\rayne.ini file. It has gamecontrol entry, which can only have one value (from what I see it's 0 for mouse and keyboard and 1 for gamepad). There is also Controller_0_type entry - with values 0 for mouse and keyboard and 2 for gamepad (and probably 1 for joystick, but I can't verify it).
The interesting part is that there are entries for Controller_1_type, Controller_2_type and Controller_3_type, but I don't see a way to make them work at the same time.
The only thing that may help is Controller_0_pc_stick entry - you can try setting it's value to 1 if it isn't set already, but I'm afraid it won't help. It's still worth a try.
(And I don't have the GOG version, so this entry may not even be there).

You'd have to map the joystick buttons to keyboard keys...
Still - why would you want to do that ? I imagine you want to move with the joystick and aim with the mouse... Why not simply use a k+m combo instead ?

For analogue movement I guess. Neither using a keyboard nor binding joystick buttons / axes to keys will solve it.