Ultrasound computed tomography (USCT) has the potential to detect breast cancer by measuring tissue acoustic properties such as speed-of-sound (SOS). Current USCT image reconstruction methods for SOS fall into two categories, each with its own limitations. Ray-based methods are computationally efficient but suffer from low spatial resolution due to neglecting scattering effects, while full-waveform inversion (FWI) methods offer higher spatial resolution but are computationally intensive, limiting their widespread application. To address these issues, a deep learning (DL)-based method is proposed for USCT breast imaging that achieves SOS reconstruction quality comparable to FWI while remaining computationally efficient. This method leverages the computational efficiency and high-quality image reconstruction capabilities of DL-based methods, which have shown promise in various medical image reconstruction problems. Specifically, low-resolution SOS images estimated by ray-based traveltime tomography and reflectivity images from reflection tomography are employed as inputs to a U-Net-based image reconstruction method. These complementary images provide direct SOS information (via traveltime tomography) and tissue boundary information (via reflectivity tomography). The U-Net is trained in a supervised manner to map the two input images into a single, high-resolution image of the SOS map. Numerical studies using realistic numerical breast phantoms show promise for improving image quality compared to naïve, single-input U-Net-based approaches, using either traveltime or reflection tomography images as inputs. The proposed DL-based method is computationally efficient and may offer a practical solution for enhancing SOS reconstruction quality, which could potentially improve diagnostic accuracy.