Robot learning has proven to be a general and effective technique for programming manipulators. Imitation learning is able to teach robots solely from human demonstrations but is bottlenecked by the capabilities of the demonstrations. Reinforcement learning uses exploration to discover better behaviors; however, the space of possible improvements can be too large to start from scratch. And for both techniques, the learning difficulty increases proportional to the length of the manipulation task. Accounting for this, we propose SPIRE, a system that first uses Task and Motion Planning (TAMP) to decompose tasks into smaller learning subproblems and second combines imitation and reinforcement learning to maximize their strengths. We develop novel strategies to train learning agents when deployed in the context of a planning system. We evaluate SPIRE on a suite of long-horizon and contact-rich robot manipulation problems. We find that SPIRE outperforms prior approaches that integrate imitation learning, reinforcement learning, and planning by 35% to 50% in average task performance, is 6 times more data efficient in the number of human demonstrations needed to train proficient agents, and learns to complete tasks nearly twice as efficiently. View https://sites.google.com/view/spire-corl-2024 for more details.