CSS background-blend-mode multiply with opacity - css

Question

I'm porting a UI-based game from Unity to Cordova. In Unity, I was tinting predominately white images with various colors to reuse assets. The rough CSS equivalent seems to be using the [mostly standard] background-blend-mode property set to multiply and have the image in the background with the desired tint color as the bg color.
.tinted {
background-image: url('theimg.png');
background-size: 100% 100%;
background-color: #0f0;
background-blend-mode: multiply;
}
The problem is that it doesn't preserve the opacity of the image, namely the transparent parts become the tint color. The spec says something about blending from the top down so I thought it might relate to blending with the bg color, but it doesn't work if I layer a solid color (as a gradient) on top of the image either.
.tinted2 {
background-image: url('theimg.png'), linear-gradient(to bottom, #0f0, #0f0);
background-size: 100% 100%;
background-blend-mode: multiply;
}
Reversing the order of the background images or changing the blend mode to normal, multiply or multiply, normal doesn't work either. Any suggestions on how to do this correctly using CSS?
EDIT: As the answer mentions, the alpha aspect can be achieved using the mask property. I used a combination of the two techniques to get what I needed:
.tintedMasked {
background-image: url('theimg.png');
background-size: 100% 100%;
mask-image: url('theimg.png');
mask-size: 100% 100%;
background-color: #0f0;
background-blend-mode: multiply;
}

Answer 1

If I understand correctly what you're trying to do, then background blending is not the way, but masking.
div {
height: 200px;
background-image:linear-gradient(SlateBlue, Tomato);
-webkit-mask: url(https://cdn.pixabay.com/photo/2016/12/28/19/37/denied-1936877_960_720.png) top left no-repeat / contain;
mask: url(https://cdn.pixabay.com/photo/2016/12/28/19/37/denied-1936877_960_720.png) top left no-repeat / contain;
}
}
<div></div>
<h1>No stairway??</h1>
That's assuming your mask images are alpha transparent PNGs. you could also use luminance mask by setting mask-mode: luminance;