Bridges or culverts on roads on district lines, except as provided in Section 5-503 of this Code, shall be constructed and repaired by such districts and the expense of such construction and repair shall be borne in proportion to the assessed value of the taxable property in the respective districts according to the last preceding equalized assessment thereof prior to such construction or repair; or the commissioners of such adjoining road districts may enter into joint contracts, which may provide for any just division of cost. Such contracts may be judicially enforced against such commissioners jointly, the same as if entered into by individuals, and such commissioners may be proceeded against jointly by any parties interested in such bridges or culverts, for any neglect of duty in reference to such bridges or culverts, or for any damage growing out of such neglect.