openstreetmap - Using OpenLayers maps with SSL

I am using OpenLayers map by using the hosted JavaScript:

But my client has SSL installed and when I try to run my map page it shows:

(2)[blocked] The page at https://domain.com/rwd/ ran insecure content 
   from http://openlayers.org/api/2.13.1/OpenLayers.js.

So I tried https one and it turns out openlayers doesn't have one

https://openlayers.org/api/2.13.1/OpenLayers.js

Then I download the Openstreet js and hosted in client server, but then all the styles and related images are lost. Although it does show the map, basically numerous warnings pop-up in the console and I'm afraid this might get rejected at play store or so. I'm developing a hybrid application which runs on server as well.

Warnings now :

The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://b.tile.openstreetmap.org/14/8743/5624.png.
The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://b.tile.openstreetmap.org/14/8742/5624.png.
The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://c.tile.openstreetmap.org/14/8743/5623.png.
The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://b.tile.openstreetmap.org/14/8743/5625.png.
The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://c.tile.openstreetmap.org/14/8744/5624.png.
The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://a.tile.openstreetmap.org/14/8742/5623.png.
The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://c.tile.openstreetmap.org/14/8742/5625.png.
The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://a.tile.openstreetmap.org/14/8744/5623.png.
The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://a.tile.openstreetmap.org/14/8744/5625.png.

The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://a.tile.openstreetmap.org/14/8743/5622.png.
The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://c.tile.openstreetmap.org/14/8742/5622.png.
The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://c.tile.openstreetmap.org/14/8745/5624.png.
The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://b.tile.openstreetmap.org/14/8744/5622.png.
The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://b.tile.openstreetmap.org/14/8745/5623.png.
The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://c.tile.openstreetmap.org/14/8745/5625.png.
The page at https://domain.com/rwd/#/customer-plot/234 displayed insecure content from http://c.tile.openstreetmap.org/14/8745/5622.png.

GET https://domain.com/rwd/js/lib/theme/default/style.css 404 (Not Found) 
/*This the corresponding stylesheet that is loaded via Openstreet.js*/ 

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I tried with cdn with SSL and still same issue:

https://cdnjs.cloudflare.com/ajax/libs/openlayers/2.11/OpenLayers.js

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I downloaded the entire GitHub repo for Openstreet thinking this will solve the image and CSS issue.

https://github.com/openlayers/openlayers

While the above solved the CSS issues, the map however is shown by loading out images from another external site tile.openstreet.com. Seems like I have to dig into openstreet js as well..:(..

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Important : I am using backbone.js.

Note : I have gone through OpenLayers 2.12 and http basic authentication woes and that has not helped me. I do not have any control over the server configuration. I just have access to a folder where I need to set up the website an everything else works fine, but this SSL is troublesome.

Changed real website address to avoid Google linking it.