Is it normal to get a job offer call, after interviewing and passing the background with an employer?

Yes, that means you were being considered for the job, but other circumstances within the company made it impossible to hire you at that point. So now there is a job opening, they called you. If it is better than what you have, take it. Jobs are very scarce right now, so consider your self lucky!!

Some firms take their sweet time about it to be sure they're getting the best person. Or their plans may have been delayed, e.g. by the recession. In this job market I wouldn't ask too many questions if I were you.