I cannot get the blend or mix actuators to work in my Captiva?

The voltages you show sound like the feedback circuit that tells the module the position of the actuator. The actuator motor however is a 12 volt unit that uses reversing polarity to move. Take a simple test light and check the fuses that supply the module, Those are the Run2 and the HVAC fuses in the instrument panel fuse box. One should have battery voltage full time the other is switch with the ignition. Do the indicators and other controls in the module work, there is a two wire ground and one of those could fail as well. All of them are in connector X2 on the module. The Brown wire on terminal 2 is a switched power, the Red/white wire on terminal 4 is a full time hot. Then the Black wires on terminals 3 and 10 are the grounds. Check those and see what you have.
You replaced the module? Did you also program it using SPS so that it would work? Then do the actuator calibration? Both require a scan tool to do.

Well to do the programming you need a dealer level tool that can handle J2534 protocol or a laptop with GM MDI/GDS on it. There are multiple ones out there but be setting down when you price them. For the recal it's simple, open the scan application, go to the HVAC module and select the re-calibration. It then erases the learned values, moves the actuator through full travel and records those levels as the new open/closed.