It's known to be what they call "multifactorial polygenic inheritance" which means you have to hit on a combination of genes in the mother and a combination of genes in the father. This won't happen in all pregnancies, because only half the paternal and maternal genes make it into any given blastocyst.
So, say I had to have the genes for chronic hypertension plus an immune mediated condition, and DH had to have the genes for a slightly deranged implantation in the set that were in that particular spermatazoa, and when you put all of those together, the pregnancy is preeclamptic.
This could happen in the third pregnancy, or the second pregnancy, for the first time. It's also the case that some women will develop underlying conditions as they age - chronic hypertension or autoimmune conditions are the likely culprit here - and that those underlying conditions mean the implantation of an otherwise normal placenta isn't tolerated by the mother's body.
So, short answer: yes, but also the mother.