Transverse modes beyond the fundamental mode are increasingly being explored to increase information capacity in both mode-division multiplexing and high-dimensional quantum information processing. The ability to combine and separate these modes at arbitrary ratios over a broad bandwidth is central to these applications. Motivated by the lower bending loss and intermodal crosstalk of partial Euler bends in multimode waveguides, we develop a geometric framework based on partial Euler bends for broadband power coupling between the first two transverse electric modes on a silicon-on-insulator platform. Our methodology uses a hybrid of eigenmode expansion and finite-difference time-domain methods. Our designs feature a mode (de)multiplexer, as well as unbalanced couplers (2/3 and 1/3 splitters). The simulated 1-dB bandwidths of our directional couplers range from 101 nm to 134 nm. The best-performing fabricated mode (de)multiplexer has a measured 1-dB bandwidth of 90 nm, a conversion efficiency of 94.0% and crosstalk below -18 dB at 1550 nm. Our results validate the use of partial Euler bends for broadband transverse mode directional couplers and provide a general framework for their design.