Why is there a milky residue under my radiator cap after overheating?

I appreciate any help on this.

To clarify, this is an '03 Mazda Protege. The car overheated and some smoke came from under the hood. I checked it out and my coolant from the reservoir had shot out and was empty. Under the radiator cap (I waited before checking this) there was chunky white precipitate around the gasket (the cap is fine and seals well).

Anyways, I drained the coolant and it was a darker, murky green. I drained the oil and the oil looked fine. I recently changed the transmission oil and the dipstick appeared still bright red and no green.

I'm assuming no transfer occurred from the coolant, into the block, since there was no separation in the oil. This is why I'm not sure if it's the gasket or something else. I do understand that the pressure of the oil will be higher than that of the coolant, so that is likely why the coolant is darker now.

Additionally, I checked my reader and got code P0117, which is likely just due to the coolant having gotten too low. Also, I changed the coolant last year, so it shouldn't be bad, unless two coolants mixed and reacted somehow.

Sorry to hear...

Sounds like a head gasket...

The combustion chamber pressure will be the highest psi, then the oil system pressure, and finally the cooling system pressure.

Head gaskets can blow in many different ways:

one way is where the cooling system gets pressurized by the combustion chamber pressure. This combustion air will then displace the coolant and force too much of it into the overflow, causing the overflow bottle to in itself overflow, and after the car shut down, there is now air in the system, and not enough coolant is left to cool the engine...then you get an overheat, then more coolant is forced out, it is a vicious cycle....

Since you had an overheat, you need to find out why...

You have already drained and refilled the coolant and changed the oil, so Kudos to you for that!

next I would want to:

verify that all air is bled / burped from cooling system
verify there are no cracks in the overflow bottle
verify that both of the electric cooling fans operate
verify thermostat is operating properly
verify that temp sending unit is operating and that the fan clicks on as soon as you disconnect the sensor plug

if you need to dig deeper, you can pull the spark plugs and read them to see if you are indeed burning coolant as well.

Ditto to what mazdadude said, sounds like a head gasket.

My wife and step-daughter both drive Subarus and I've done head gaskets on both,
one of them twice (didn't get the heads resurfaced the first time). The primary symptom
on them is bubbles in the coolant overflow bottle, followed by the bottle overflowing when
the breach gets really bad. Most leak internally from combustion chamber into the cooling
system, some leak externally.

Different engine designs have different vulnerabilities, but I haven't had any issues with my P5
in 14 yrs/208K miles.

Monitor your coolant level closely, both the overflow and the radiator itself. If you aren't losing
any and it doesn't overheat again you may have dodged a bullet. If it becomes a recurrent
problem it's probably time for a head gasket, possibly a new head.

Also, I believe most auto shops can check your coolant for signs of combustion gasses.