I know a bunch of liberal arts schools which have engineering program and which are pretty good. They have been sending most of their students to good graduate schools with plenty of lab experience in their belt. It all depends on what school you go to.
On the other hand, I don't think Bachelors in engineering or something like that will really make it easy to get  a job in that field. You need much more (probably ME) than that to stand a good chance. At the same time, there are plenty of job opportunities related to chemistry n bio majors...just consult your career services job database.