During your conversation with HR about a potential job offer, if they happen to ask how much you were earning at your previous job, can you also include the signing bonus? Something like, "I was earning $XXX per year, as well as a $XXX signing bonus", or should you just mention the salary?
When HR or a recruiter asks you about salary, they're generally looking for two things: (1) ongoing compensation expectations or history, and (2) any specific amounts that they might need to overcome -- money that you will lose if you leave your current job.
If your signing bonus, tuition, 401(k) match, or other bonus is contingent on you remaining with the company, then you should mention that along with your salary, keeping them separate. If your signing bonus was a one-time thing, you've met the obligations that came with it, and it wasn't a huge amount, it's better to leave it out so the recruiter doesn't think you're trying to artificially inflate your salary by combining a one-time payment with an annual payment.
If you receive an annual bonus in addition to salary, do mention that -- even though it's (presumably) not committed to the same level that your salary is, it's an expectation and history that you have.
Here's approximately what I say when I'm in this position (and have decided I'm willing to disclose my salary in the first place, which is a separate question):
My current salary is $X, and the annual bonus is usually between Y% and Z%. I'll lose a 401(k) match of $A if I leave before (date).