What does "impossibly ill suited" mean?

I'm having trouble understanding this sentence "on the marriage of one of her step-sons to a princess of high rank when the couple were impossibly ill suited". What does "impossibly ill suited" mean? Does it mean they are very well suited or they are so not suitable for each other?

Solution 1:

In this case, it means that the relationship was totally unsuitable.

Ill-suited essentially means that they were not right for each other.

The function of "impossibly" in the phrase is as an intensifier. It's saying that no amount of give-or-take surrounding the match is going to make the situation acceptable.