It may seem like there's no way to use the TV headphone jack without the sound switching off, but it's easy to make the sound come from headphones and speakers at the same time. Most TVs are designed so that the speaker switches off when headphones are plugged in, as this is how many people use headphones, but there is a way around this. Usually you would do this because two people want to listen at different volumes.
Find a good position for the speakers near your TV. Arrange the speakers so that the left speaker, right speaker and your listening position make a triangle with roughly equal sides. Adjust the height so that the tweeters are roughly the same height as your ears.
Find the headphone socket on your TV. Plug your 3.5mm stereo plug to 2 x 3.5mm stereo sockets adaptor into the headphone socket. Plug the lead from your speakers into one of the sockets on the adaptor.
Use another lead if you have a separate amplifier: plug the RCA connectors of your 3.5mm mini plug to RCA audio cable into the socket marked "CD In" or another line level input, then plug the 3.5mm mini plug into one of the sockets on the adaptor.
Plug your headphones into the other socket on the adaptor. Switch on your speakers and your amplifier if you have one. Make sure the volume is not turned up too high, then switch on your TV. Check the sound is coming from the speakers and the headphones. Adjust the volume of the speakers to the level you want. Adjust the final position of the speakers to find the best listening position by adjusting between the three position ideas given in step 1.
Don't have the sound too loud when you listen with headphones.