I'm sure it depends on where you are from.
My Obgyn referred us to a Reproductive Encrinologist(spelling?) for some infertility issues. The RE referred us to a genetic counselor, when he saw our past.
My first baby was stillborn at around 30 weeks with seemingly no reasons.
The genetic counselor ran a blood test on me to check for 160+ genetic disorders. DH and I had already had our general chromosomes checked and both had come back fine.
My test came back that I was a carrier for one thing, but it wasn't anything that is common or fatal/disease causing. So, we decided to not go through with testing on my husband (as a carrier he'd have to have the same thing to pass it on - and I had no blaring issues).
She also talked to me about my family and DH's family background. It would help to have him there! My DH couldn't get off work. She worked out a family tree to spot any risks, etc. It was a very pleasant appointment and I'm glad we could get an idea of things before getting into pregnancy again!
Good luck!