You could do this to add the background image with a 50% opacity black overlay to the Home page body:
body.home:before {
content: '';
position: absolute;
top: 0;
left: 0;
width: 100%;
height: 100%;
z-index: -1;
background-image: linear-gradient(rgba(0,0,0,0.5), rgba(0,0,0,0.5)), url(https://full_URL_TO_BACKGROUND/image.jpg);
background-size: cover;
}
Not sure how your design is intended to be – but you will need to make any other containers with a background color transpatent as well e.g
body.home .site {
background-color: transparent;
}