In this paper, we study the asymptotic throughput capacity of a static multi-channel multi-interface infrastructure wireless mesh network (InfWMN) wherein each infrastructure node has m interfaces and c channels of unequal bandwidth are available. First, an upper bound on the InfWMN per-user capacity is established. Then, the feasible lower bound is derived by construction. We prove that both lower and upper bounds are tight. We limit our analysis for more practical case of$\mathrm{m} \le \mathrm{c}$. However, for the asymptotic upper bound, our analysis can be used for the general case in which there is no constraint on m and c. Our study shows that in such a network with Ncrandomly distributed mesh clients, Nrregularly placed mesh routers, and Nggateways, the asymptotic per-client throughput capacity has different bounds, which depend on the ratio between the total available bandwidth for the network and the sum of m first greatest data rates of c available channels, i.e.,$\sum \limits_{\mathrm{j} = 1}^\mathrm{C} \mathrm{w}_\mathrm{j} / \sum \limits_{\mathrm{j} = 1}^\mathrm{m} \mathrm{w}_\mathrm{j}$. The results of this paper are more general compared to the existing published researches. In addition, in the case that$\mathrm{w}_\mathrm{i} = \mathrm{W}/\mathrm{c} \forall \mathrm{i},\mathrm{}1 \le \mathrm{i} \le \mathrm{c}$, our results reduce to the previously reported studies. This implies that our study is comprehensive compared to the formerly published researches.