Quick note on this:
cr.mp is a great button for these situations, but you have to WAIT until they cross to the other side before doing the input. cr.mp is good at beating a cross-up, but if you do it while still facing the side they started the jump from, of course it’ll come out the wrong way. This is more a matter of you needing to delay your timing for the move to be effective, rather than the move not working to deal with these situations. If you know they’re going to cross up, you should do a slight walk forward under the jump, and then you can cr.mp the other way, no problem.
Here’s a tip if you’re struggling with this -
Go to training mode, pick R. Mika vs. M. Bison, then set the dummy to Playback recording.
Record Bison doing the following string - forward dash, forward dash, c.lk, c.lk, c.mp, forward jumping mk
The two dashes are to close to point blank. From there, the string spaces perfectly for the j.mk to cross you up.
Get the dummy to start running this sequence (I just did), and then block the first three hits and work on beating the cross up jump. You’ll find that all of the following will work:
Walk under, c.mp
Walk under, LK Wingless
Walk under, f+hp (which can crush counter if your timing is good)
Walk under, s.hp
Also, if you’re worried about being able to time your walk under and attack to beat the cross-up, you can also react to the cross-up jump by using c.hp. This won’t hit or give you any damage, but the low hitbox on c.hp combined with its forward movement puts you out of range and their cross-up will whiff.
The point is, cross ups aren’t that hard to deal with if you recognize the situations and react accordingly.
Incidentally, I think s.hp might be R. Mika’s best ground-to-air normal for beating jumping attacks coming from the front (c.mp is better for attacks coming more from above). It looks like s.hp has a hitbox that extends in front of its hurtbox, which gives it really good properties for beating other attacks as they come down. This move doesn’t look like it should be a good anti-air, but as others have noted it seems to be one of her better tools.