It's not a horrible match for Jax if you learn how to ground pound underneath sai. Timing that IN LAG however.... good fuckin luck!
He's definitely one of the only characters that really gives her any resistance.
JAX
As I said, learning to ground pound under Mileena's sai is very important to winning this match. There is a video on youtube of DVD's Jax demonstrating how to do that. It really shows how Jax has the potential to absolutely own Mileena if played perfectly. Trading wave punches with her sai is a pretty good tactic. Remember that any time you block her telekick or roll, you can JK/backbreaker for big damage. Once I land that combo with him, I usually just wave punch since I have a life lead. Gotcha grab is useless, Mileena can get a hop kick in unblockably afterwards. Anti-air HK her out of jump ins. This is really tough, but very important. Usually when Mileena does a jump forward air sai, she will sai early on in the jump. You have to watch for that, and aaHK if she actually jumps in without sai-ing. Golden punches are good are eliciting blocked rolls/telekicks from lesser Mileenas, but vs tough Mileenas, you just end up eating lots of chip damage. In general, keep away from her. But if she tracks you down, send her a message with a HK to the face. Or a multi-slam- always nice. Crouch punch to keep her away when she inches close.
MILEENA
An elite Jax can be a tough cookie to crack for Mileena. Mix up the sai both ground and air, and at various heights. Do not get too spammy, or Jax will start timing his ground pounds underneath them. Air sai from around sweep distance are really hard for Jax to ground pound under, so mix up your screen positioning when you sai (don't get predictable). Rolls are very good vs Jax because he's usually not blocking to avoid taking chip damage. But use them cautiously- if he blocks, you're about to lose around half your life. Telekick just gets you in trouble, only use it as a surprise tactic. Get in and CQC, she can certainly mess him up with all her in-close attacks. Don't forget Mileena has a really beasty combo on Jax = anti-air HP, roll, telekick. Massive damage, and looks bad ass. Sweep him often!
7-3 for Mileena. She has the better specials, sweep and CQC. Jax isn't far behind her, but still:
King Jax bows before Queen Mileena.