My husband and I have not lived together for over 10 years

Until you have a written Separation Agreement or an Order of the Court, you are not legally separated. If you wish to be legally separated, you should find a local attorney to assist you.

Not legally.

Unfortunately you are not legally separated with out documents reflecting the separation.

Legally no. You have to be living separate and apart pursuant to a written validly signed separation agreement or judgment of separation. The good news is that you can file for divorce on the grounds of irretrievable breakdown of the marriage. The bad news (or good, depending upon which party you are) is that ALL marital property acquired during the period of your separation is in the proverbial marital pot for equitable distribution. Consult an attorney to find out the definition of marital and separate property and how equitable distribution works, particularly for those couples not living together for lengthy period of time.

You are certainly "separated" informally, but legally you are only "separated" once a valid separation agreement is executed, or a court decree of separation is issued. If you've been separated that long, it may be time to cut the cord & file for divorce. Schedule a consult with a Bronx Divorce attorney for a full assessment.