It would make them both safer
Generally speaking (that's important!), antibodies do not grant immunity. They grant resistance. If enough people enjoy that resistance then society becomes immune ("herd immunity"). Diseases like polio, scarlet fever, and measles were declared overcome due to so many having the antibodies and didn't start to rear their ugly heads again until the blankety-blank anti-vaxers started claiming they had the right to threaten the herd.1
What has happened is important to understand. Because antibodies provide only resistance, not immunity, anybody can get sick when a chink in the herd-immunity armor is created. It would be convenient if all the anti-vaxer's children were the people getting sick, but just as COVID-19 has underscored the complications of asymptomatic carriers, the reality is that the anti-vaxer children become the foothold, but not necessarily the place where the battle is fought.
But even if we ignore the anti-vaxers, it's always possible for an individual to become ill from a disease for which they have antibodies. All those diseases I mentioned (and a great many more) were statistically wiped out, but not completely. Occasionally someone would contract polio, scarlet fever, or measles.
This is why Jane and her baby would be safer, but not necessarily immune.
Frankly, put a person teeming with antibodies in a room full of sick people related to those antibodies and the odds are quite good that person will get sick — but the antibodies do make it quite a bit harder. Concentration of exposure, length of exposure, general strength/health of the body, age of the body, etc, all have an impact, too.
However, if what you're looking for is a rationale to keep Jane and her baby safe from a disease in your story — antibodies are a perfectly good suspension-of-disbelief solution to the problem.
1 I need to be fair. What they're claiming is parental rights to determine the medical assistance and/or interference government can impose on their children. In almost any other context, that would be an important and valuable demand. Unfortunately, this is perhaps the one and only context where it's such a bad idea that We, The People might need to impose societal authority.