This is a major problem with drow, yes.
Drow kind of... suck as player characters. Particularly at low levels. Their special racial qualities aren’t exactly amazing, and the LA +2 is extremely burdensome. Their stats are all-around low, particularly HP, skills, and saves, and the most fancy thing about them, the Spell Resistance, is a hindrance more often than not. Unfortunately, particularly early on, Wizards of the Coast greatly over-valued Spell Resistance.
The best solution, therefore, is to use the lesser drow from Player’s Guide to Faerûn or Wizards’ website instead of the “full” drow from Monster Manual. They lose some benefits (−2 Con, +2 Dex rather than +2 Dex, +2 Int, for example), but they’re also LA +0, and hey look: no Spell Resistance. Good news all around. Strongly recommended.
The only real major loss is that they don’t have darkness as a spell-like ability, which strikes me as kind of odd. Yeah, it’s pretty good for an LA +0 race, but it’s iconic and it’s really not too much. Particularly with the elves’ typical −2 Con, which kind of ruins a lot of elven races. So I recommend giving that back to them, 1/day. If the DM really thinks it’s necessary, making it an altered form of darkness that doesn’t block darkvision eliminates any significant balance issue even relative to the weaker LA +0 races.
Failing that, remember that Spell Resistance can be lowered. It takes a Standard Action to do so, which sucks, but if your drow is down, but not out, and you’re healing after combat, it will cover a lot of situations.
For the rest of the time, Spell Penetration isn’t a terrible feat (and one you might get use out of anyway), but if you have Spell Compendium, you could instead use the assay spell resistance spell, for a whopping +10 vs. Spell Resistance. It’s a 4th-level spell, so it sucks to use it just to heal up the drow, but considering how annoying SR can be for your other spells, it’s not a bad idea to prepare it for them, and if it ends being “wasted” healing the drow, oh well.
Stabilizing with the Heal skill is about all its good for, and the odds of a character falling between −1 and −9 get extremely low as creatures deal more and more damage, so I would not recommend any significant investment for that circumstance (this is also why Diehard is a weak feat). But if you end up in that situation, Heal is usable untrained: feel free to make Wisdom checks against DC 15; the odds are a far cry better than the 10% chance the drow has of stabilizing on her own (and she still gets to try that, too).
In general, healing is a primarily out-of-combat activity until you get the heal spell, because the healing spells (particularly the cure spells) are too inefficient to use in combat (you will prevent more damage by killing an enemy faster than you will ever manage to heal). Even if the drow is bleeding out, which will become more and more rare as you gain levels, you’ll probably have multiple checks with your +6, or you’ll be able to dig out your wand of cure light wounds and zap the drow a few times until you get past the SR. It’ll suck, taking a long time and probably wasting a lot of money, but unfortunately that’s a drow’s lot in 3.5. You might want the drow to be buying a replacement wand for the party if she’s wasting too many charges.