I'll start off by saying I do not work on jets with truly sophisticated autopilots, but I can get you started. With a couple of specific exceptions that are irrelevant to what you are doing, all autopilots that have pitch control have an Altitude Hold mode. This mode usually uses a signal from a baro/static pressure-sensing device such as the Air Data Computer or a dedicated Altitude Capsule (supplied by the A/P manufacturer); the pilot has to first establish the a/c at the desired altitude and then engages the ALT HOLD mode, the autopilot will then maintain the a/c at the specific static pressure at which the mode was selected, usually by using the pitch trim. If the QNH changes the pilot will have to change altitude and then re-select ALT HOLD (this of course does not happen with airliners or other higher-performance a/c that cruise above 11 000' and use 1013.25mB/29.92"Hg as their reference pressure).
If the pilot of an a/c fitted with one of the better A/Ps wants to change the level of the a/c, say to descend from FL180 to FL140, then he/she could dial in 14 000' on the Altitude Preselector/Alerter and the A/P will descend the a/c and level off at FL140. On the a/c I work on, the APA
uses the Mode C Grey Code outputs from the Encoding Altimeter and is therefore only able to control the altitude to the nearest 100'.
The next mode all decent muti-axis A/Ps have is APPROACH. This mode is selected/armed prior to commencing the approach to an airport and when the A/P is fed a Valid Glideslope Deviation signal (which is actually two signals, the Deviation Signal itself and a separate Flag signal) from the G/slope receiver, the A/P changes from Armed to Capture and maintains the a/c on the Glideslope.
There is also VERTICAL SPEED Mode, but the A/Ps I am familiar with do not have this mode. AFAIK the a/c will climb or descend at a certain Vertical Speed as selected by the pilot; I think the input signal is a rate-of-change-of static pressure from the Air Data Computer.
photo below shows a King Air instrument panel, you can see the Altitude Preselector/Alerter to the left of the radar display.
Monty Python's Flying Circus has nothing to do with aviation, except perhaps for Management personnel.