It's partly about the volume but also about the range of frequencies the guitars cover.
An electric guitar (if distorted) covers from quite low - almost bass up to higher middle ('harsh') - quite a broad range and can be a piercing sound if one string is played at a time.
An acoustic guitar covers a broader upper range (you probably notice the "tinkly" higher end of the acoustic over the electric, which is often the magic of an acoustic & electric playing together :-D ), but acoustic overpowers things is it's too loud in the mix so tends to sit little lower in volume.
So while your friend has a point, it's possible to get around it.
The "normal chord playing" part sounds like it's well in control already - no need for change there, I assume.
For solos, consider having an effects box, as Rockin Cowboy suggests. However I'd go a bit beyond just a volume boost. You might find these pedal effects useful:
A compressor : Keeps the sound clean, but fills it out by making quiter parts louder so that the overall sound is nice and even. This will help a lot when playing a solo on an acoustic as it also helps with sustain, which some acoustic guitars lack. Be careful though - too much compression will cause the guitar to feed back through its body, as it tries to make "any" signal louder.
Distortion/Overdrive - if you can't beat 'em join 'em ! Distortion works quite well on an acoustic for solos, if that's a sound you're after. Possible further issues with feedback though.
Most importantly: Graphic equaliser. This could do lots of jobs for you:
1) You can normally set them so that the overall volume is a bit higher than when switched off, so it could help boost the sound for solos
2) You might find as you turn up for a solo, the guitar wants to feed back, normally at the same frequency depending on amp position/room size etc. You can use the graphic eq to turn that feedback frequency down a touch, thus muting the feedback.
3) It'll enable you to choose a goot 'voice' for the guitar while you're soloing. Eg if your electric friend is chugging away on a distorted guitar, you'll possibly need a bit more middle range to help the acoustic punch through a bit.
If it's a question of straight volume, let the amps do that part (or a boost pedal) - I've found the worst thing is to try to project the sound by playing the guitar harder. It normally sounds awful and disappointing, and is much harder to play like that than in your usual comfort zone.
I'd say if you can afford the outlay, try a compressor (mild) and graphic eq. If not, go with Rockin Cowboy's suggestion & just boost the sound a bit.
The alternative is to have everyone else pipe down a bit while you solo - this is a great effect once or twice but it's a bit weird if you do it too often. The song may lose its mojo unintentially.