Hopefully a Florida attorney will give you some Florida-specific advice, if it differs from my advice at all, but since FMLA is a federal law, and employee benefits like STD are governed by federal employee benefits law (ERISA), I don't think the answer changes if you're in FL or TN, where I am licensed.
Basically, FMLA and STD shouldn't have anything to do with one another. If your job is protected by FMLA, the fact that you file for STD shouldn't affect the FMLA protections at all. Also, STD should not be denied because you're on FMLA. The one worry that I have for you is that I don't know what your job is, what it requires, and what your medical condition is. There's a possibility that at the end of your FMLA protected leave, if you want to return to work, but your employer has reason to believe you're not capable of doing the job yet, they may not allow you to return. In that case, if you believe you can return, you may find yourself in a fight. If you think you could return to work with accommodations (under the Americans with Disabilities Act), you should be sure to discuss that with your supervisor and suggest specific accommodations which you think would allow you to return to work.
Jeremy Bordelon is a licensed attorney in the State of Tennessee only, and is authorized to practice in all Tennessee State and Federal courts, and before the Social Security Administration in any jurisdiction. Please call our firm at 1-866-959-5362 if you would like to discuss your case in more detail. The answers provided on Avvo.com are for information purposes only, and should not be relied on as legal advice. This answer does not create an attorney-client relationship between us. In some jurisdictions, this answer may be construed as attorney advertising.
If you have worked with your employer for a year or more, you are entitled to 12 weeks of FMLA leave for a qualifying serious health condition. Whether you qualify for short term disability benefits (STD benefits) is a different matter which is governed by the definition of "disability" in the STD contract.
If you receive STD benefits while you are on a qualified FMLA leave, it will not affect your right to have up to 12 weeks of FMLA leave. Most employers will count the first 12 weeks of any medical leave as FMLA leave, as most employers want you to use up your 12 weeks of FMLA leave as soon as possible. As long as you are back at work in 12 weeks or less, you should be ok.