Most folks mic the cab in a regular manner, and then run a direct box like a Countryman at the same time. The mic will be routed through your mixer or whatever other mic pres you have to the recorder and the DI is usually routed through a second channel on the console or a second mic pre ..

Watch out for phasing issues as well as the mic'ed signal will arrive later than the DI signal. You should be able to adjust the timing after recording however if you are using a software-based DAW.