As a voice teacher, all I can say is practice, practice, practice. There is no easy way to do this.

Truthfully, all singers have this problem to start with. The best way to overcome it is to blend these voices into one. How do I do this? I'm glad you asked. First, I assume that you are doing your breathing exercises everyday and are using your diaphragm. What you need to do is stretch your head voice and your chest voice to cover each other. When you do your scale exercises sing as high as you can in your chest voice. Concentrate on raising this note by note day by day. Conversely and most importantly, sing in your head voice to the lowest note your can reach without switching. Keep trying to lower this daily note by note. You should be able to smooth your transition between these two "voices."

OR you can just change keys so that you are singing in your own range (tessitura) rather than the key that the instruments are comfortable playing in.

May I finally suggest that you spend some money on a good voice teacher (not a vocal coach) who can show you some good exercises (like octave splits) to correct this problem. Sorry this post is so long but you can see I am passionate about the voice.