Welcome to the PICAXE forum.
The outputs you are looking at are likely those from the darlington transistor array which are open collector switches, and can only 'short to ground', sink current rather than output current / voltage. Connect the output via a 1K to +V and you will see what you expect.
If you put your meter on the appropriate PICAXE legs ( taking care not to short them to one another ) you will see the actual outputs switching high and low.