We demonstrate a smartphone-integrated handheld detection instrument capable of utilizing the internal rear-facing camera as a high-resolution spectrometer for measuring the colorimetric absorption spectrum, fluorescence emission spectrum, and resonant reflection spectrum from a microfluidic cartridge inserted into the measurement light path. Under user selection, the instrument gathers light from either the white "flash" LED of the smartphone or an integrated green laser diode to direct illumination into a liquid test sample or onto a photonic crystal biosensor. Light emerging from each type of assay is gathered via optical fiber and passed through a diffraction grating placed directly over the smartphone camera to generate spectra from the assay when an image is collected. Each sensing modality is associated with a unique configuration of a microfluidic "stick" containing a linear array of liquid chambers that are swiped through the instrument while the smartphone captures video and the software automatically selects spectra representative of each compartment. The system is demonstrated for representative assays in the field of point-of-care (POC) maternal and infant health: an ELISA assay for the fetal fibronectin protein used as an indicator for pre-term birth and a fluorescent assay for phenylalanine as an indicator for phenylketonuria. In each case, the TRI-analyzer is capable of achieving limits of detection that are comparable to those obtained for the same assay measured with a conventional laboratory microplate reader, demonstrating the flexibility of the system to serve as a platform for rapid, simple translation of existing commercially available biosensing assays to a POC setting.