If you got married on 9/25/2015, and lived with your husband for even one day then you were not allowed to file as HOH for 2015. You could file as Married Filing Jointly, if your spouse agreed, or Married Filing Separately, but NOT as HOH.

If you were legally married as of 12/31/2015, your choices were Married Filing Jointly, if your spouse agreed,  or Married Filing Separately, unless you meet the qualifications to be "considered unmarried", in which case you could file as Head of Household. The requirements are:

Considered Unmarried
To qualify for head of household status, you must be either unmarried or considered unmarried on the last day of the year. You are considered unmarried on the last day of the tax year if you meet all the following tests

1. You file a separate return

2. You paid more than half the cost of keeping up your home for the tax year.

3. Your spouse did not live in your home during the last 6 months of the tax year. Your
spouse is considered to live in your home even if he or she is temporarily absent due to special circumstances.

4. Your home was the main home of your child, stepchild, or foster child for more than half the year.

5. You must be able to claim an exemption for the child. (There are some exceptions to this rule, see IRS Pub 17, Chapter 2 and 3) You can find Pub 17 at this link
http://www.irs.gov/pub/irs-pdf/p17.pdf

The answer is the same for 2016. If you are married and live with your husband you can not legally file as Head of Household, and you can not ever claim your spouse as a dependent.

You can file as Married Filing Jointly even if your spouse has no income.

You need to file an amended return for 2015; filing as Married Filing Jointly, adding your husband as spouse (not as a dependent).

How to amend: <a rel="nofollow" target="_blank" href="https://ttlc.intuit.com/questions/1894381-how-to-amend-change-or-correct-a-return-you-already-filed"...>

I can still file MFJ even though I wasn't even married for over half the year? Also, do I file MFJ even though he doesn't have an income? How is this possible?

You can file as MFJ even if you got married on the last day of the tax year. Your filing status is determined by your marital status as of the last day of the tax year. When you file as MFJ, there is no requirement for both of you to have income. "How is that possible" - that is the tax law, pure and simple.
You can find the detailed requirements of the tax law in IRS Publication 501, at this link:
<a rel="nofollow" target="_blank" href="https://www.irs.gov/pub/irs-pdf/p501.pdf">https://www.irs.gov/pub/irs-pdf/p501.pdf</a>

According to the list you provided me, I still don't understand why  I'm not eligible for HOH. I paid more than half the cost of keeping the cost, I wasn't married until September 29, my home was home, and I filed myself and the children in the previous years. And, obviously wasn't married, so I filed with me and the children.

What do you mean that you weren't married? You said that you got married on Sep. 29, so you were married as of the last day of the tax year and that is all that matters.

I was trying to say that I didn't get married until Sept 29. Sorry for the confusion. So, if I didn't get married until December 31, then I wouldn't be married? But, if I married any date prior, then I would be considered married?

Even if you got married on  Dec, 31 you would be considered married for the entire year.