Antigenic characterization based on serological data, such as Hemagglutination Inhibition (HI) assay, is one of the routine procedures for influenza vaccine strain selection. In many cases, it would be impossible to measure all pairwise antigenic correlations between testing antigens and reference antisera in each individual experiment. Thus, we have to combine and integrate the HI tables from a number of individual experiments. Measurements from different experiments may be inconsistent due to different experimental conditions. Consequently we will observe a matrix with missing data and possibly inconsistent measurements. In this paper, we develop a new mathematical model, which we refer to as Joint Matrix Completion and Filtering, for HI data integration. In this approach, we simultaneously handle the incompleteness and uncertainty of observations by assuming that the underlying merged HI data matrix has low rank, as well as carefully modeling different levels of noises in each individual table. An efficient blockwise coordinate descent procedure is developed for optimization. The performance of our approach is validated on synthetic and real influenza datasets. The proposed joint matrix completion and filtering model can be adapted as a general model for biological data integration, targeting data noises and missing values within and across experiments.