I have exome sequencing data and as far as I know, it should include all exonic regions including the mitochondrial genome. When I blast my sequences to recover mitochondrial protein-coding genes, I get a ton of intermittent stop codons and a lot of gaps which I generally do not find when extracting nuclear genes. The literature tells me it includes all exomic region so I am wondering if this is just a coverage problem or something else? I don't work with mitogenomes generally but after extracting the popular COI gene exons, and aligning everything to the reference sequence the columns of stop codons makes no sense to me.
Why don't you check the coverage of the mitochondrial genes (those having a reasonable non-multimapping MAPQ like > 20 or so) to see if those genes are included.
As you probably know there are different kits for WES. So please be as specific as possible. For each kit the design files should be available, although some will be easier to find than others. In general I would expect those genes to be included... Although targeting these might lead to severe unbalanced coverage...