I have a case in which the defendant gave a recorded statement/confession. The defense attorney is objecting that the comments from my officer's during the taking of the statement are hearsay and not admissible. For example... Officer says, " I just got off the phone with the ER doctor and he said that the baby's head was severely beaten." or " I just talked to your neighbor who said...."
My response is that those statements are not being offered for the truth of the matter asserted but simply to give context to the conversation and to what the defendant is responding to. Does anyone else have a different idea or case law? The defense attorney is stating that the jury can hear his client's response only and NOT the hearsay comments by the investigating officers.

You're correct that they are admissible and not hearsay because they are not offered for the truth of the matter asserted.

Kirk v. State, 199 S.W.3d 467

Defense will be entitled, if they ask for it, for a limiting instruction that the statements by the officer is not evidence for the truth of the matter asserted, but it still comes in to give context to the answers.