Background image jumps when address bar hides iOS/Android/Mobile Chrome

I've got a similar issue on a header of our website.

html, body {
    height:100%;
}
.header {
    height:100%;
}

This will end up in a jumpy scrolling experience on android chrome, because the .header-container will rescale after the url-bar hides and the finger is removed from screen.

CSS-Solution:

Adding the following two lines, will prevent that the url-bar hides and vertical scrolling is still possible:

html {
    overflow: hidden;
}
body {
    overflow-y: scroll;
    -webkit-overflow-scrolling:touch;
}

This issue is caused by the URL bars shrinking/sliding out of the way and changing the size of the #bg1 and #bg2 divs since they are 100% height and "fixed". Since the background image is set to "cover" it will adjust the image size/position as the containing area is larger.

Based on the responsive nature of the site, the background must scale. I entertain two possible solutions:

1) Set the #bg1, #bg2 height to 100vh. In theory, this an elegant solution. However, iOS has a vh bug (http://thatemil.com/blog/2013/06/13/viewport-relative-unit-strangeness-in-ios-6/). I attempted using a max-height to prevent the issue, but it remained.

2) The viewport size, when determined by Javascript, is not affected by the URL bar. Therefore, Javascript can be used to set a static height on the #bg1 and #bg2 based on the viewport size. This is not the best solution as it isn't pure CSS and there is a slight image jump on page load. However, it is the only viable solution I see considering iOS's "vh" bugs (which do not appear to be fixed in iOS 7).

var bg = $("#bg1, #bg2");

function resizeBackground() {
    bg.height($(window).height());
}

$(window).resize(resizeBackground);
resizeBackground();

On a side note, I've seen so many issues with these resizing URL bars in iOS and Android. I understand the purpose, but they really need to think through the strange functionality and havoc they bring to websites. The latest change, is you can no longer "hide" the URL bar on page load on iOS or Chrome using scroll tricks.

EDIT: While the above script works perfectly for keeping the background from resizing, it causes a noticeable gap when users scroll down. This is because it is keeping the background sized to 100% of the screen height minus the URL bar. If we add 60px to the height, as swiss suggests, this problem goes away. It does mean we don't get to see the bottom 60px of the background image when the URL bar is present, but it prevents users from ever seeing a gap.

function resizeBackground() {
    bg.height( $(window).height() + 60);
}

I found that Jason's answer wasn't quite working for me and I was still getting a jump. The Javascript ensured there was no gap at the top of the page but the background was still jumping whenever the address bar disappeared/reappeared. So as well as the Javascript fix, I applied transition: height 999999s to the div. This creates a transition with a duration so long that it virtually freezes the element.