Well, this sounds like a level mismatch problem. What amp are you using? If it doesn't have a LINE OUT or a kind of DI OUT (whatever they want to call it), then I strongly advise you to NOT use that headphones output, it just isn't designed for that purpose, even if you succeed in matching the levels, the sound will suck
The best you can do is to use a microphone on your amp (even a "cheap vocal one" will do alright, but not 5$ of course

), it is actually how guitars are usually recorded professionally!
If you don't have a mic or you don't want to deal with all the concerns it brings (levels, position, eq, etc...), then you'd better just plug your guitar straight into the mixer!

Yes, it's not a stupid idea, especially when you are not using any effect or pedal. Think about that: 90% of electric guitar sound on John's solo records before 2004 are done like that, and even on BSSM album, and if you want another example, Dave Gilmour's Another Brick In The Wall solo it's recorded with a Les Paul with P90s straight into the mixing board, and then it was added some compression and reverb/echo AFTER!
Of course you can add any post recording editing you like, or even use some "real time processing software" like Guitar Rig, but I have no experience with those programs.
Feel free to ask if you have any doubt!
PS: Nice image