Weird question, live amp sound and simultaneous DI?

Yes, you can do that.
Several options:

1) Your guitar into a splitter/splitting DI. One signal to your recording interface, the other one into the amp. Then you can record both signals, Amp/Mic and DI. But be carefull, splitting changes impedance which leads to sound changes with passive pickups.

2) Guitar directly into a recording interface. Routing the Input signal to an Output and there through a reamp box into the Amp. So you can record the DI signal and the Amp/Mic.