The exponential growth in data traffic and dramatic capacity demand in fifth generation (5G) have inspired the move from traditional single-tier cellular networks toward heterogeneous cellular networks (HCNs). To face the coming trend in 5G, the high availability requirement in new applications needs to be satisfied to achieve low latency service. Usually, these applications require an availability of six nines or even higher. In this paper, we present a tractable multitier multiband availability model for spectrum aggregation-based HCNs. We first derive a closed-form expression for the availability of spectrum aggregation-based HCNs using the signal-to-interference-plus-noise model. By doing so, we formulate two optimization problems, one is to maximize the average availability, and the other one is to minimize the average power consumption. These two optimization problems are both nonconvex problems, which are challenging to solve. To cope with them, we propose to apply genetic algorithm for the joint user equipment (UE) association, subcarrier assignment, and power allocation problem. Our results show that the average availability in spectrum aggregation-based HCNs improves with decreasing number of UEs, as well as increasing power budget ratio. We also show that increasing the maximum number of aggregated subcarriers decreases the average power consumption, but cannot guarantee the substantial improvement of average availability.