I doubt this is really an error – as this interface is USB-powered, the designers probably spec'd the headphone output with rather low maximum voltage, so as to avoid supply problems; I know at least the old Tascam US-x2y series suffered from that problem. For consumer headphones, which are targeted at low-voltage battery-supplied devices and hence have very low impedance, this should still give you a sufficiently loud signal, but with studio headphones it's often a bit dissapointing.
Input-monitoring is in particular a problem if the input comes straight from a mic without any compression, saturation, EQ whatsoever: this way, it'll sound quieter than anything on a recording, but still have a lot of peak level.
One thing you should ensure is that the high peaks don't just come from artifacts you'd have to filter away later anyway: low frequency plops, and high-frequency hisses. In doubt, use suitable spiders, pop-killers and improve the mic placement to maximise "useful level", that will give you both better monitoring level and probably better sound on the recording.
In particular for vocals, it can also be a good idea to put a tube preamp before the interface. That warm, smooth overdrive is pretty much standard for studio vocals, and makes the signal considerably "hotter" without increasing the required peak headroom. You might also put in a gentle compressor for yet louder RMS without any distortion, I used to do that a lot – but now I rather prefer to do all that later in software, where you have much finer-grained control.
The most straightforward solution to your problem at hand however would tackle the other end: put an externally-powered headphone amplifier on the line out, and don't use the built-in one at all! Dedicated headphone amps should always give plenty enough volume, so you can just make the outputso loud you have good monitoring and then adjust the DAW playback level to get the mix right.