Sounds to me like the amp is humming not the mic. AC hum is common with high gain amps because they contain so many stages, any low levels of AC EMF get amplified to audible levels. Any gain pedals and their associated power sources can be the cause, any cord and the guitar itself, especially guitars with single coil pickups or fender guitars that are wired with unshielded wires.
The reason you hear it when recording is because your ear isn't directly in front of the speaker like a mic is. if you're micing an amp sitting on the floor, all your hearing is the indirect sound reflecting around the room. You want to either tilt the amp back at your ears or raise it up to ear level so your ears hear the sound beaming at them directly like the mic is hearing it. If there's hum there you'll know it. You can then dial up tones and gain levels that help mask the problem. Make sure the room doesn't have dimmers or florescent lights too. Finding the source of hum is like being a detective. you need to rule out causes one by one till you find the cause. Even then it might be staring you right in the face but you're unwilling to deal with it.
Hum can also come from the tubes needing to be biased if its a tube amp or from a ground loop. Sometimes just getting your computer and all gear on the same outlet ends all hum problems. Generic wall warts is a big one. Boss pedals need zero hum wall warts or the will hum both on and bypasses because they are not true bypass, they are buffered pedals which are always on. Cheap guitar cords are a huge cause of hum. Cords with 75% shielding may be OK plugged straight into an amp with no pedals, kick in a drive pedal and they hum like a banshee. You want to use cords with 90% copper shielding or better. A noise gate/Hush pedal can do wonders quieting hum when you stop playing.
The guitar itself can have either copper foil or conductive paint added to ground the hum out. Inexpensive guitars can usually be helped with this quite a bit.
The interface itself may be humming but the likelihood is pretty low. The preamps in it are not exactly high gain so I cant see them raising any kind of hum up unless its being fed that hum at its input. If anything you may hear some hiss when the preamp's maxed out but hum is unlikely. If the unit uses and external wall wart then make sure its the right one. If the current isn't right or its not smoothing the DC you may get it to leak into the circuit.
If the units getting pure DC there's no way the unit should be humming unless its a piece of crap poorly designed and lacks shielding. Even then its more likely an environmental issue overcoming the unit, not the unit itself generating it because the unit is DC, not AC. If you have a higher end interface with an AC to DC power supply built in and the units getting older then maybe the smoothing caps are getting old.
The mic itself? I've used SB57's for 50 years never had one hum, ever. The cables? Sure a bad cable or connector with a bad ground could do it but you'd likely be loosing allot of signal gain too. Mic cable qualities are usually pretty good even with the cheaper ones. Main differences being how strong the signal winds up being and how durable the connectors are. The mics themselves are housed in a huge chunk of metal. There no way you can get hum to penetrate it if its grounded. A bad wire inside it would go dead, not hum.