Hydraulic hybrid vehicles are inherently power dense. Power-split or hydro-mechanical transmissions (HMT) have advantages over series and parallel architectures. In this paper, an approach for optimizing the configuration and sizing of a hydraulic hybrid power-split transmission is proposed. Instead of considering each mechanical configuration consisting of combinations of gear ratios, a generalized kinematic relation is used to avoid redundant computation. This captures different architectures such as input coupled, output coupled and compound configurations. Generic kinematic relations are shown to be mechanically realizable. Modal operation of the transmission is introduced to reduce energy loss. The Lagrange multiplier method for computing the optimal energy management control is shown to be computationally efficient for use in transmission design iterations. An optimal design case study indicates improvement in fuel economy and smaller component sizes for the compound and input coupled power-split configurations.