The rapid advancement of Large Language Models (LLMs) has opened new possibilities for intelligent multi-agent systems capable of autonomously performing complex tasks. To build such multi-agent systems, developers can leverage LLMs for task-solving, tool interaction, and code generation but should manage their costs and unpredictability. This experience paper introduces COPMA, a model-based approach to enabling continuous human-LLM co-programming of multi-agent LLM applications. COPMA uses ``feature-block" models to track application features and their implementations as agents and code blocks. Supported by co-programming patterns, it guides developers in constructing, refining, and refactoring feature implementations through trial-and-errors with LLM agents, leveraging their feedback, suggestions, and code examples. The patterns guide the shift of feature implementations between agents and code to balance flexibility, predictability, and cost. Our experience in developing LLM agents for collecting and reviewing medical research papers demonstrates that human-LLM co-programming can reduce development effort and achieve stable behavior to enable rapid prototyping of multi-agent LLM applications