Family samples, which can be enriched for rare causal variants by focusing on families with multiple extreme individuals and which facilitate detection of de novo mutation events, provide an attractive resource for next-generation sequencing studies. Here, we describe, implement, and evaluate a likelihood-based framework for analysis of next generation sequence data in family samples. Our framework is able to identify variant sites accurately and to assign individual genotypes, and can handle de novo mutation events, increasing the sensitivity and specificity of variant calling and de novo mutation detection. Through simulations we show explicit modeling of family relationships is especially useful for analyses of low-frequency variants and that genotype accuracy increases with the number of individuals sequenced per family. Compared with the standard approach of ignoring relatedness, our methods identify and accurately genotype more variants, and have high specificity for detecting de novo mutation events. The improvement in accuracy using our methods over the standard approach is particularly pronounced for low-frequency variants. Furthermore the family-aware calling framework dramatically reduces Mendelian inconsistencies and is beneficial for family-based analysis. We hope our framework and software will facilitate continuing efforts to identify genetic factors underlying human diseases.