The rapid rise of power conversion efficiency (PCE) of low cost organometal halide perovskite solar cells suggests that these cells are a promising alternative to conventional photovoltaic technology. However, anomalous hysteresis and unsatisfactory stability hinder the industrialization of perovskite solar cells. Interface engineering is of importance for the fabrication of highly stable and hysteresis free perovskite solar cells. Here we report that a surface modification of the widely used TiO2 compact layer can give insight into interface interaction in perovskite solar cells. A highest PCE of 18.5% is obtained using anatase TiO2, but the device is not stable and degrades rapidly. With an amorphous TiO2 compact layer, the devices show a prolonged lifetime but a lower PCE and more pronounced hysteresis. To achieve a high PCE and long lifetime simultaneously, an insulating polymer interface layer is deposited on top of TiO2. Three polymers, each with a different functional group (hydroxyl, amino, or aromatic group), are investigated to further understand the relation of interface structure and device PCE as well as stability. We show that it is necessary to consider not only the band alignment at the interface, but also interface chemical interactions between the thin interface layer and the perovskite film. The hydroxyl and amino groups interact with CH3NH3PbI3 leading to poor PCEs. In contrast, deposition of a thin layer of polymer consisting of an aromatic group to prevent the direct contact of TiO2 and CH3NH3PbI3 can significantly enhance the device stability, while the same time maintaining a high PCE. The fact that a polymer interface layer on top of TiO2 can enhance device stability, strongly suggests that the interface interaction between TiO2 and CH3NH3PbI3 plays a crucial role. Our work highlights the importance of interface structure and paves the way for further optimization of PCEs and stability of perovskite solar cells.