Future wireless infrastructure networks will dynamically access spectrum for maximum utilization. However, the fundamental challenge is how to provide stable spectrum access required for most applications. Using dynamic spectrum access, each node's spectrum usage is inherently unpredictable and unstable. We propose to address this challenge by integrating interference-aware statistical admission control with stability- driven spectrum allocation. Specifically, we propose to proactively regulate nodes' spectrum demand to allow efficient statistical multiplexing while minimizing outages. Admitted nodes coordinate to adapt instantaneous spectrum allocation to match time- varying demand. While the optimization problem is NP-hard, we develop computational-efficient algorithms with strong analytical guarantees. Experimental results show that the proposed approach can provide stable spectrum usage while improving its utilization by 80-100% compared to conventional solutions.