Load Balancing Web Proxy Servers

we don't see clearly if applying an http-transparent profile could be good in our case.

i understand it does forward invalid http packet instead of dropping. anyway, it is okay if http profile works fine in your case.

The Transparent Proxy Mode enables the BIG-IP system to forward invalid HTTP traffic to a specified server, instead of dropping the connection. By configuring an HTTP profile to forward invalid HTTP traffic, you can manage various atypical service provider scenarios, such as HTTP traffic from non-browser clients that function as web browsers.

Manual Chapter: HTTP Profiles (Proxy mode)