Most horticultural guides I've read recommend not planting blackberries and raspberries near each other because they will spread diseases between each other. How far apart do they need to be to prevent contamination? Is the opposite side of the yard (e.g. 30 feet) enough? Or do I need to try to figure out a way to incorporate one of them into my front yard landscaping?
The likelihood of disease is not more likely when planted in close quarters, but if one species contracts a disease, it will likely pass it on. To avoid this, planting them apart should do it, anywhere that no blown leaves/running soil will reach them.
Now I don't worry about it myself, I put everything together. Disease control in untreatable diseases just means having a fast cull reflex. :)
Now, another thing to consider is that blackberries (in my area) often spread by underground stems, and sucker all over the place. The raspberries don't. They are usually a bigger plant than raspberries, so might invade and outgrow them. Apparently this is the opposite of how they grow in the UK, if I read Bamboo's answer properly.
Frankly, I don't agree with the premise that blackberries and raspberries planted together are more subject to disease. I've worked in many gardens where blackberries are trained up a trellis or fence (being large, trailing plants), with raspberry bushes 3-5 feet in front, in the same bed. The only drawback with it is that raspberries tend to spread by underground runners or rhizomes, and pop up 1 or 2 feet away, which means they 'march' and spread over an area. This sometimes can mean they get too close to the blackberry, but it isn't usually a problem - they tend to 'march' to where its brighter rather than darker in terms of light. For this reason though, its common for raspberries to be grown in a dedicated bed or area, possibly with a root rhizome barrier around the edges to contain them. Even so, provided there is a suitable support to tie the blackberry into, there's no reason why a blackberry or two cannot be included in the same bed.
Both plants require plenty of sun and similar soil conditions - note that strong fertilizers should be avoided because both produce quite a lot of roots near the surface, and these can be burned by too strong a fertilizer.
No separation is needed for raspberries and blackberries. You may be confusing blackberries with black raspberries. Black raspberries are subject to anthracnose fungus which may be aggravated by red raspberries. I planted black raspberries about 100 ft away from reds; the blacks still had some anthracnose but no more than if there were no red raspberries in the area. A friend grew blackberries and red raspberries adjacent on the same fence , no fungus problems with either . Full disclosure ; I grew ""Bristol" black raspberries 40 years ago , today maybe GMO has worked its magic and developed fungus resistant black raspberries.