Multiple Criteria Lookup With Date Range Match?

I am trying to create a formula that will lookup multiple criteria within a table, one of those criteria being a date that falls within a certain date range. The purpose of the data is for billing tenants and owners in a building. I have successfully been able to use Index Match to lookup 2 criteria, one of them being a specific date match (see my attachment). However, I need to add a third criteria looks up the date that falls between a specific date range. The concept is to run a query where I enter a Unit (apartment) number into one cell, a Billing Date into another cell and the Type (Owner or Tenant) into a third cell to determine the Name of the person who fits these criteria... Criteria A Lives in Apt XX, Criteria B Who's lease start date and end date is inclusive of the Billing Date that I entered and Criteria C who matches the Type of customer, either Owner or Tenant.