How does one know, as a spouse, if one could qualify as head of a house hold? I am the person who takes care of most of the home expenses- bills, mortgage, car payments?

If you are legally married and living with your spouse you cannot file as Head of Household.  You can only file as Married Filing Jointly or Married Filing Separately.

If you are legally married and NOT living with your spouse for the last six months of the year AND you have a qualifying child as a dependent and meet other requirements, then you are considered unmarried for tax purposes and can file as Head of Household.

See this TurboTax support FAQ for HOH when married - https://ttlc.intuit.com/community/married/help/can-a-married-person-claim-head-of-household-filing-status/01/26366

Head of household is designed for single parents, usually through separation or divorce. If you are legally married, you must live alone and not share your home with your spouse.  If you are married and living with your spouse, it is almost always better to file married filing jointly, even if one spouse earns most of the money.