Can I Get Covered Until I Find a Job?

I’m a teacher in NYC who is in the process of resigning from a job where I receive full health benefits and going to one where I won’t have any benefits, as a permanent substitute. My husband and I are both covered under this plan. Could we enroll in ObamaCare for a period of time? I say this because I’m looking for a permanent position as a head teacher for the 2015-2016, so I would receive health benefits starting in September.