Existing approaches to facilitate the interaction between password managers and web applications fall short of providing adequate functionality and mitigation strategies against prominent attacks. HTML Autofill is not sufficiently expressive, Credential Management API does not support browser extension password managers, and other proposed solutions do not conform to established user mental models. In this paper, we propose Berytus, a browser-based governance framework that mediates the interaction between password managers and web applications. Two APIs are designed to support Berytus acting as an orchestrator between password managers and web applications. An implementation of the framework in Firefox is developed that fully supports registration and authentication processes. As an orchestrator, Berytus is able to authenticate web applications and facilitate authenticated key exchange between web applications and password managers, which as we show, can provide effective mitigation strategies against phishing, cross-site scripting, inline code injection (e.g., by a malicious browser extension), and TLS proxy in the middle attacks, whereas existing mitigation strategies such as Content Security Policy and credential tokenisation are only partially effective. The framework design also provides desirable functional properties such as support for multi-step, multi-factor, and custom authentication schemes. We provide a comprehensive security and functionality evaluation and discuss possible future directions.