1920x1080 monitor issues

Hi everyone,

I have a Acer P216HV 21.5" 1920x1080 monitor and i've been noticing some issues when I connect it to my xbox 360.

I have a DVI-D > HDMI because my monitor doesn't have a HDMI slot.

The problems:
- When I play on 1920x1080 resolution I don't notice any crisp, clean, 1080p, it's all blurry and some of the images go low quality, even if I change it to 1280x720 it still looks the same but my native res. is 1920x1080.
- I've noticed lines in games i've played with the darks and lights that look like its not combining the pixels correctly, they look like rectangles top to bottom but with a straight color.

Questions:
- Is my monitor capable of supporting 1080p on my Xbox 360 through DVI-D > HDMI?
- Is it my monitor that's not giving the full 1080p like it should?

I really need some input guys, this is my only HD widescreen source for my xbox & computer!

Thanks.