Network estimation based on sparse inverse covariance matrices has become a useful approach to studying microbial interactions. Various methods for sparse inverse covariance estimation have been proposed for the high-dimensional setting, including graphical lasso. However, current methods do not address the compositional count nature of microbiome data, where abundances of microbial taxa are not directly measured, but are reflected by the observed counts in an error-prone manner. Adding to the challenge is that the sequencing depth is an experimental technicality that carries no biological information but can vary drastically across samples. To address these issues, we develop a new approach to network estimation, called BC-GLASSO, which models the microbiome data using a logistic normal multinomial distribution with the sequencing depths explicitly incorporated and embraces the heterogeneity in sequencing depths to correct the bias of the naive empirical covariance estimator. We demonstrate the advantage of BC-GLASSO over current methods under a variety of simulation scenarios. We also illustrate our method in an application to a human microbiome data set.