Hello Lianna, any jacket to cover both sports will be a bit of a compromise. I went with an OMM kamleika smock. I'd say it's a running jacket you can cycle in.
It's unusual in that the fabric stretches but it is properly waterproof and breathes better than non waterproof jackets I've had. It's designed to fit closely which means it doesn't flap on the bike and strangely the fabric doesn't rustle when you run. It has a chest pocket, thumb loops, drawstring waist and a hood that rolls into a collar.
The hood is adjustable and has a peak and is cut so it fits around the neck properly rather than gaping and letting the wind pull the hood back. I've found for running in rain you have to reduce the layers or you'll over heat and get wet on the inside as FB said. It won't keep you warm on the bike but layers will sort that.
For running I can't fault the jacket/smock. For cycling I've used it 4-5 hours of contiuous steady rain and it didn't let any in and it's light folds up small and easily fits in a jersey pocket. The fabric is thin enough that you can wear the hood under a cycle helmet and the peak sticks out the front just like a cycle cap.
The down sides. The sleeves are plenty long enough for cycling but if you want to use the thumb loops with gloves they're a bit tight not a major problem though, the sleeves are elasticated. The cut at the back is long enough for the jacket to cover my backside but it's a close fit rather than a drop tail that a cycling specific jacket might have.
The jacket comes in black or a sort of lilac-blue - not really stand out colours for cycling at night although there are reflective markings on the front, back and arms.
If you're cycling tri or running fashion concious you may not be impressed, this is a bit of kit used by mountain marathon and fell runners and is designed to work rather than look cool. If you don't care about that it's worth a look and is a very good compromise longer term you can always add a bike specific jacket if you need to, I use mine for running, cycling and roller skiing . It's not a cheap option-you can pick one up for £110 and there's a full zip model if that's preferable to a smock.