Recent AI code assistants have significantly improved their ability to process more complex contexts and generate entire codebases based on a textual description, compared to the popular snippet-level generation. These codebase AI assistants (CBAs) can also extend or adapt codebases, allowing users to focus on higher-level design and deployment decisions. While prior work has extensively studied the impact of snippet-level code generation, this new class of codebase generation models is relatively unexplored. Despite initial anecdotal reports of excitement about these agents, they remain less frequently adopted compared to snippet-level code assistants. To utilize CBAs better, we need to understand how developers interact with CBAs, and how and why CBAs fall short of developers' needs. In this paper, we explored these gaps through a counterbalanced user study and interview with (n = 16) students and developers working on coding tasks with CBAs. We found that participants varied the information in their prompts, like problem description (48% of prompts), required functionality (98% of prompts), code structure (48% of prompts), and their prompt writing process. Despite various strategies, the overall satisfaction score with generated codebases remained low (mean = 2.8, median = 3, on a scale of one to five). Participants mentioned functionality as the most common factor for dissatisfaction (77% of instances), alongside poor code quality (42% of instances) and communication issues (25% of instances). We delve deeper into participants' dissatisfaction to identify six underlying challenges that participants faced when using CBAs, and extracted five barriers to incorporating CBAs into their workflows. Finally, we surveyed 21 commercial CBAs to compare their capabilities with participant challenges and present design opportunities for more efficient and useful CBAs.