Will an internship in biology benefit me when my major is not biology? I'm an undergraduate majoring in chemistry. But I'm very much interested in the field of biology too.

Will an internship in biology benefit me, say when I apply for graduate school? I don't yet know what I'll be specialising in later on. If I decide to specialise in biology, then all's good. But what if I stick with something primarily chemistry? Then will it look like I don't have enough experience in chemistry?

Also, can I ask my department's HOD or any other chemistry professor for a recommendation letter while applying for the internship in biology? Since he's a chemistry professor, even if I did ask and he did write me one, will that count for much? After all, it's going to talk about my skills, etc. in chemistry, and not biology.

On the other hand, if I didn't ask him for a recommendation letter and I asked only some of the Life Sciences professors for it, will it be unethical, or would he take offence? ( I have no idea about etiquette regarding these things)
I don't want to do something that's going to get me in his bad books.
I completed undergraduate summer internships in biology although I ultimately wound up applying (and attending) graduate school in psychology. Although the internship did not directly align with my current career path, at the time it helped me narrow down my professional interests. In applying for jobs and graduate school, my internships, regardless of discipline, were seen as evidence that I was motivated, organized, and had some experience in professional settings. 

At the undergraduate level many skills (including solid record keeping, attention to detail, and proper lab technique) are transferable across scientific disciplines. Further, completing one internship outside your discipline shouldn't significantly stunt your ability to prepare for graduate school in chemistry.

Having a letter of support from any professor should be acceptable, provided it is a strong letter. In all likelihood, your advisor will know you the best and be able to write the most supportive letter. However, if a life sciences professor knows you well, a second letter or co-written letter might be helpful.