adjectives - Opposite of "mutually exclusive"

In philosophy the expression would be mutually necessary:

Definition: A necessary condition for some state of affairs S is a
condition that must be satisfied [in order to obtain] S.

Example of mutually necessary conditions:

Jack and Jill will go up the hill only if they both go up the hill.

• Jack will not go up the hill without Jill.


• Jill will not go up the hill without Jack.

so

• Jack going up the hill is necessary for Jill to go up the hill.


• Jill going up the hill is necessary for Jack to go up the hill

Jack going up the hill and Jill going up the hill are mutually necessary.

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In a broader context:

Interdependent implies a certain level of mutual necessity:

ADJECTIVE

(Of two or more people or things) dependent on each other:

OED

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Codependent relationships exhibit an intensity of interdependence that increases the sense of necessity:

Derivative of codependency:

NOUN

[MASS NOUN]

Excessive emotional or psychological reliance on a partner, typically
one with an illness or addiction who requires support:

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Symbiotic relationships do not all exibit necessary, but the mutual benefit is a specialized expression of interdependence:

derivative of symbiosis

NOUN

[MASS NOUN] Biology

1.0 Interaction between two different organisms living in close physical association, typically to the advantage of both.

There is a brand of symbiosis referred to as obligate symbiosis, which does imply the must of the OP:

In animals, a common mutualistic symbiosis occurs between many
herbivores and microorganisms of their digestive tracts. Ungulates
(hoofed animals) and some other animals eat plant material that is
high in cellulose , even though they lack enzymes capable of breaking
down cellulose molecules. They obtain energy from cellulose with the
help of symbiotic bacteria and protozoa living within their digestive
tracts. These microbes produce enzymes called cellulase that break
down cellulose into smaller molecules that the host animal can then
utilize. Similarly, wood-consuming termites depend upon symbiotic
protozoans living within their intestines to digest cellulose. These
are obligate symbioses. The termites cannot survive without their
intestinal inhabitants, and the microorganisms cannot live without the
host. In each of these symbioses, the host animal benefits from the
food provided by the microorganism and the microorganism benefits from
the suitable environment and nourishment provided by the host.

Read more:
http://www.biologyreference.com/Se-T/Symbiosis.html#ixzz3R4tP9zIU

Emphasis mine

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Synergetic, a derivative of synergy approaches the meaning you are looking for:

NOUN

[MASS NOUN]

The interaction or cooperation of two or more organizations,
substances, or other agents to produce a combined effect greater than
the sum of their separate effects: