OK, this is not uncommon, but there are workarounds.
First of all, as I learned from my good friend Spiros (which, incidentally is an electronics wiz and I believe you will see his work soon enough!) the problem seems to be with modern headphones vs the impedance of the headphone outputs on most recording interfaces. Even my rather expensive RME Fireface 400, has this problem, the sound through headphones is "tiny" compared to the "real thing".
One solution is to use a dedicated headphone amp, preferably a tube driven one, that will give back the harmonic content to the sound.
The method I employ is rather crude but effective. Simply, when I record guitar, I set channel level to a minimum and only hear the "background" channels (drums, guide lines, etc). I put "half" the headphones on my ears, in order to hear the amp sound clearly and just have a good indication of where I am in the song. One problem is input latency, in other words, the A/D converters striving to keep up with your playing and always being a little late... But on my card this is minimal.
Other times, I don't use mics at all, but employ a cabinet simulator, listening to the resulting mix through my monitors. I may leave the actual cabinet "on" in order to have the "on stage" feeling, but, in reality, I record the signal through the cab sim only. My amp has a dummy load which allows me to bypass the speakers altogether, although you can achieve the same thing with a Hot Plate or similar external dummy load.
These are the methods I employ personally, I can't insist they are the best, but they work for me...