Starting from where you are, and assuming your trio is well balanced acoustically, I would suggest you use just a good stereo pair of mics rather than getting tied up in trying to mic each instrument and the drums. You say the acoustics in your room are not good, but a pair of small diaphragm condensers (SDCs) such as a matched pair of the Rode NT55 or, for more directionality in poor acoustic, the MBHO MBNM-440CLs would get you recordings that you recognized as "your" sound.

You will have to carry out a number of trials to get an acceptable recorded balance, of course, but it should be possible to find microphone positioning that works for your trio. Some of the problems may come from deciding where to place the guitar amp and how loud to have it, and others from parts of the drum kit overwhelming the mix, so you as performers may have to adapt to a style of "playing for recording" on the occasions where you need a good audio perspective in the result.

The type of interface you get will depend on what you want to connect it to for recording on to. I was not aware that, even with the recent update to the iPad OS, you could record any audio directly to an Ipad other than via the built-in or an external mono domestic-quality microphone, but you may be able to bring me up to speed on that one. I know that GarageBand on the iPad will edit and mix captured sounds, but if you can load conventional USB drivers, you have a good choice of 2-channel USB interfaces. My pick of them would be the RME BabyFace, but this may be over your budget once you have got a pair of decent mics. The Apogee Duet is another unit worthy of consideration.

Here's my peculiar take on your question. Boswell has indicated extremely nice possibilities for you. None of which I dispute. But from a cost standpoint, along with what type of computer you may be using, my suggestion is this: you get rid of your H1 or keep it for good measure. You'll go out & purchase a new H4n. Not the original H4. You get a small camera tripod and place it in front of the drum set. You get 2 SHURE SM57's and plug those into the H4n. That model can actually record 4 simultaneous tracks. The XY small capsule condenser microphones will sound great in front of the jazz drum kit. Meanwhile, the SM57's will sound marvelous on both the bass & guitar be it acoustic or amplified. And with that, you have the ability to record live, anywhere, 100% conveniently. You'll also have the ability to utilize it as a digital audio interface of a high quality nature with your computer. It's simple, clean, versatile & quite portable. It also makes financial sense in a struggling world economy for everyone.

The cool part also is that you'll be able to remix in software however you want. And you'll be able to create a variable acoustic sounding recording that way by creating different stereoscopic feelings of the guitar, bass, drum set with just a couple of single microphones on single tracks. You can then also utilize the device if you wanted to add a vocalist after a recording session with the jazz group. Utilizing the XY stereo microphones and a single solo vocal microphone to 3 additional tracks in software and/or within the unit itself which is also possible to do. That device is an amazing bang for the buck. So we are talking about a total of less than $500 US for all of that.

I'm into practicality and good sound
Mx. Remy Ann David

Hey! While recording your group with the H4n, into its onboard memory chip, you could also take your H1, put it on the extreme opposite side of your room to capture the ambience onto its internal memory chip. Then you can dump both of those into your computer for a much liver 6 track recording. Because of the nature of these beasts, these independent recorders will actually synchronize quite nicely in your software timeline. Adjusting the H1 tracks forward or retarded in time will then present a completely different acoustical sounding environment right in your basement! Take your H1 down to your local pub and record the ambience of the pub and people without any background music. Then add that also to your recording in your timeline which will have you guys playing in front of a lovely audience. That's Hollywood baby! And you can utilize that kind of technique in recording. Think about it, try it out. You could even use the ambience of your local Wal-Mart store provided they don't have any background music playing or any other restaurant establishment. Just remember to always utilize the .wav file recording option over the MP3 standard. I wouldn't even give a damn if I was restricted to 16 bit over 24 bit in that type of an application as long as you set your levels correctly to begin with. This is where all of the technical blah blah doesn't hold water or make a damn bit of difference. You want performance value.

Always out of the box here
Mx. Remy Ann David