For in vivo studies of influenza dynamics where within-host measurements are fit with a mathematical model, infectivity assays (e.g. 50% tissue culture infectious dose; TCID50) are often used to estimate the infectious virion concentration over time. Less frequently, measurements of the total (infectious and non-infectious) viral particle concentration (obtained using real-time reverse transcription-polymerase chain reaction; rRT-PCR) have been used as an alternative to infectivity assays. We investigated the degree to which measuring both infectious (via TCID50) and total (via rRT-PCR) viral load allows within-host model parameters to be estimated with greater consistency and reduced uncertainty, compared with fitting to TCID50 data alone. We applied our models to viral load data from an experimental ferret infection study. Best-fit parameter estimates for the "dual-measurement" model are similar to those from the TCID50-only model, with greater consistency in best-fit estimates across different experiments, as well as reduced uncertainty in some parameter estimates. Our results also highlight how variation in TCID50 assay sensitivity and calibration may hinder model interpretation, as some parameter estimates systematically vary with known uncontrolled variations in the assay. Our techniques may aid in drawing stronger quantitative inferences from in vivo studies of influenza virus dynamics.