interstitium

(medicine) An interstitial space within a tissue or organ.

(medicine) Specifically the tissue between the pulmonary alveoli and the bloodstream.

(philosophy) A state between systems or spaces.

An interstice, the interval of time required by the Roman Catholic Church between the attainment of different degrees of an order (pluralised as interstitia for the overall policy, which is also occasionally spelled instertitia).