Interstitial fluid is the fluid between cells in tissues - forming the medium between cells and capillaries. From what I gather, the typical human has 5L of blood and 11L of interstitial fluid. This raises an interesting question. If I get cut, why do I not bleed interstitial fluid?
When humans are cut, generally their capillaries open and blood comes out. But this should also allow the interstitial fluid to come out - so why don't we see it?
For fluid to flow from a wound there needs to be a significant pressure gradient between where it is now and the outside of the body. Your skin generally does not have a strong compressive effect, which is why a deep cut exposing fat will not lead to the fatty tissue being expulsed from the body any more than the interstitial fluid is.
Blood, however, flows. For it to circulate there needs to be a pressure gradient between where it is now and where it is going. Since veins (including the vena cava, which channels blood back into the heart) do not have vascular walls strong enough to create a suction effect (i.e. lower pressure than the surrounding tissue), you can conclude that the pressure of blood vessels is always higher than that of surrounding tissues, and thus higher than the pressure outside of your body. This is why all blood vessels, including veins, will bleed, whereas less pressurized systems such as interstitial fluid will not.
Besides the answer by TheChymera, there's also the "problem" that interstitial fluid can't really flow freely.
Blood runs in veins, allowing to quickly circulate through your entire body. And if you cut yourself (and cut one or more veins), there is a direct path for the blood to take.
Interstitial fluid, however, has to creep through all kinds of small openings, not having a free path. Compare driving on the highway (crowded though it might be) and crawling through houses in a crowded city. Sure, if you're an experienced parkour-athlete you can get through. But if everyone wants to get out of a city, getting out over the highway will be the fastest.
By the way, there is one situation where you may "bleed" interstitial fluid: in a blister.
Here, the waterproof (and interstitial-fluid-proof) part of your skin detaches, and the fluid can accumulate. But it will do so only slowly, creeping through some small openings.
And the fact that it comes in slowly is also what makes a blister a problem, as it also means it can't flow back quickly. So if you press on it, it feels like some trapped fluid, even though you could in principle keep on applying pressure and push it back.