Almost certainly yes, the data exists. Virtually all jail phone calls and video visits are recorded and the recordings are retained. The question is whether and how that data can be accessed by the inmate or their attorney.
For inmates requesting copies of their own call or visit recordings, the process typically runs through the jail administration. Your husband would need to submit a formal request through the proper channels at Elkhart County Jail, most likely through his case manager, the records office, or the jail administrator. There may be fees associated with pulling and copying the data.
More commonly, attorneys request these recordings as part of legal proceedings. If your husband has legal representation and there is a specific reason the recordings are needed for his case, that request coming from the attorney carries more weight and may move through the system faster.
Either way, the starting point is contacting the jail staff directly and asking about the formal process for requesting communication records. They will know whether it is feasible and what is required to make the request.