I think it means, "something happened that was halfway between a slip and a fall." It was partly like a slip, and partly like a fall.
In this context, "slip" and "fall" are almost synonymous, so I personally find this particular example a little odd - even as a native speaker, I'm not exactly sure what contrast the author intends between the two words.
However, you can use similar constructions in other contexts:
He half-ran and half-walked down the street.
This one is easier to understand: He moved in a way that was halfway between walking and running, or possibly even alternated between walking and running. In my opinion, this example is easier to understand, but it is the same principle as the one in your sentence.