What you describe is also commonly called a housing cooperative, in which you don't directly own the home or apartment in which you live, but rather own stock or membership interest in the organization that owns the property and that stock or membership interest gives you a right to live in one of the apartments or homes as your residence.
Under Treas. Reg. § 1.121-1(b)(1), a housing co-op interest is considered to be an interest in a personal residence. That means the sale of your member interest in the coop will qualify for the exclusion of gain (up to $250,000 or up to $500,000 if married and filing a joint return) under Internal Revenue Code (IRC) § 121, assuming that you owned that interest and lived in the coop unit for at least two of the five years immediately preceding the date of sale and you've not sold another property in the last two years that qualified for that exemption.
But it also means you are not a first-time homebuyer for the up to $8,000 first-time homebuyer credit under IRC § 36. In order to qualify for that credit, you must not have owned an interest in a personal residence at any time in the 3 years preceding the date of purchase. Under IRC § 36, personal residence means the same thing as it does under IRC § 121. Thus, your ownership of the coop interest is an interest in a personal residence for the purpose of IRC § 36 and will disqualilfy you from this credit.