Different areas of the country seem to have different definitions as to "Condo" vs. "Townhouse" vs. "House." Try:
Albuquerque Home Rentals, Homes for Rent in Albuquerque NM, Apartments, Houses for Rent, and Rental Homes in Albuquerque, New Mexico
This website is for Albuquerque rentals. Be sure to click on "Houses & Homes" as well as "Townhouses & Condos." Just the latter will get you two or three in the whole city. There are many, newer, and smaller homes that have all the attributes of townhouses as most define them. One or two story...one or two garages.
Someone mentioned "detached" garages...they are all but unknown in Albuquerque, except in much older neighborhoods. Also, a great many of the "Townhouse" type homes are of the Pueblo-style, "flat-roofed" variety here. You either love them, or hate them. There are pros and cons to both traditional and flat roofs...like in everything else in life! :-)
I hope you enjoy your time spent in Albuquerque. You will find "many" rentals on this site, using the above "adjustments" in your search.
Best of luck!