How to prevent audio hum on a microphone circuit

I bought an electrect microphone at Sparkfun (datasheet) and built the following circuit.

When I hook it up to a professional audio interface it works but I'm having a few problems that I need to solve.

Problem 1: I'm picking up a lot of 60Hz hum. None of my other pro mics that I hook up to the audio interface pick this up so I'm positive it's coming from my circuit. To be fair, the pro mics cost up to $2K so I'm sure they have some built-in magic to prevent this. Or maybe -most likely- I'm doing something wrong since this is my first audio circuit ever.

In order to solve this I tried adding this high pass filter that I found on Google:

What happened when I tried the high pass filter was that the sound does indeed loose a lot under 150Hz but it also looses power and the signal arriving at the audio interface is very weak. Not only that, the hum is still there. It sounds like the signal from the mic is filtered but not the hum.

**Problem 2:**The signal from the mic should never reach the audio interface unless I press a button (this is called a "talkback mic" in recording studios). So I tried adding a switch like in this schematic:

The problem with this is that while it kills the signal from the mic, the hum is still there so it's not completely cutting the signal. When I added two switches to both ends of the battery, the signal and the hum go away. Is this the proper way of "killing" the circuit or should I use a DPST switch?

The wiring to the microphone is picking up 60 Hz AC radiation. It is essential to use shielded wire (i.e. microphone cable) for connections to the microphone and all other low level circuitry. Make sure that the outer shield is connected directly to ground. That means you can't use a switch as shown.

Make sure that the outer shield is connected directly to ground

Thanks! Doing this completely removed the hum.

Now the only problem left is to solve the mute switch. Any ideas?

Use the switch to disconnect the 9V battery, or short the interface input to ground, if it will tolerate that.

You said earlier that I can't use the switch as shown. What's the proper place to put it?

You cannot have the switch disconnect the microphone from the ground, as shown in your third schematic, because you need to keep that side of the microphone connected to ground via the shielded cable. So, you use the switch to disconnect the battery from the resistor. JohnLincoln is right -- you need to reconnect the capacitor as shown in his diagram.

Perfect. Thank you all for your help!

My prototype is up and running with no hum and a working switch.