Does your organization have and audit committee? Is it supposed to have one? Even if the answer is "no" I do recommend you have one in addition to your Finance Committee. The nice folks at the AICPA have put together a tool kit just for your audit committee to help them get there job done. From the website:
Audit committees have a big job to do in an organization—tough when the members have other responsibilities and the audit committee role is a part-time job with huge accountability. The AICPA Audit Committee Toolkit: Not-for-Profit Organizations is the needed help for audit committees to do the job they need to do as effectively and efficiently as possibly.You can find the kit here with details on all of its elements. For those of you who don't want to download all this info you can buy it as well.