I was able to do a quick test with both sensors connected. The barometric altitude together with the GPS altitude is shown in the plot below.
There are some discrepancies at the lower altitudes that I will need to work on a bit more. The coefficients for converting raw values from the sensors to the actual altitude and airspeed are calculated experimentally so some tuning may be required.
The source code was also released. This is code I am using to test the sensors and does nothing more than sending the altitude and airspeed data to the GCS. The next step will be to modify the airborne code to make use of the airspeed (for example maintain constant airspeed by adjusting the throttle).