Optical see-through head-mounted displays (OST HMDs) typically display virtual content at a fixed focal distance while users need to integrate this information with real-world information at different depth layers. This problem is pronounced in body-proximate multi-display systems, such as when an OST HMD is combined with a smartphone or smartwatch. While such joint systems open up a new design space, they also reduce users' ability to integrate visual information. We quantify this cost by presenting the results of an experiment (n=24) that evaluates human performance in a visual search task across an OST HMD and a body-proximate display at 30 cm. The results reveal that task completion time increases significantly by approximately 50 % and the error rate increases significantly by approximately 100 % compared to visual search on a single depth layer. These results highlight a design trade-off when designing joint OST HMD-body proximate display systems.