bwa mem performs split read alignment and, for the reads where the breakpoint is indeed in the middle, will report two alignments for the one read. I've found that bwa doesn't report them all. I found that feeding the non-split-read soft clipped alignments back into bwa gives additional split read alignments not initially reported by bwa. I've already written a program (gridss.SoftClipsToSplitReads) to do this.

On a higher level, have you considering using a structural variant calling program to detect your breakpoints? There's over 50 general purpose NGS SV callers and I'm sure at least some are likely to fulfill your requirements. Many of these tool authors (such as myself) will have already considered some data complexities/artefacts that you may not be aware of. For example, are you aware that in the presence of certain sequencing errors and/or micro-homologies, bwa will align reads with long soft clips to position A, reads with medium length soft clips to position B, and reads with short soft clips to also to position A? I've encountered cases where positions A and B are 15bp apart. If your SV detection analysis/tool is not aware of this, you might think you have two different insertion events when in reality, it's just an alignment artefact.

TLDR: use a soft-clipped/split-read based called such as CREST, Gustaf, Socrates, SoftSV, or GRIDSS. I recommend GRIDSS as my benchmarking indicates it produces the best results (followed by CREST, although the CREST call set is conservative).