You can split the signal with either an active or passive splitter.
Passive splitters may cause hum with certain combination of amps.
Active splitters may, but should not, alter the tone somewhat.
A cool thing you can do if you have stereo pedals like phasors or delays, is to use the amps in stereo. Very cool for ping pong delay effects.
Plugging into the headphone jack means muting the first amp. Just that your signal will still go through the first amp's amplifier stages.