  A unified energy principle approach is presented for analysing the
magnetohydrodynamic (MHD) stability of plasmas consisting of multiple ideal and
relaxed regions. By choosing an appropriate gauge, we show that the plasma
displacement satisfies the same Euler-Lagrange equation in ideal and relaxed
regions, except in the neighbourhood of magnetic surfaces. The difference at
singular surfaces is analysed in cylindrical geometry: in ideal MHD only
Newcomb's [W. A. Newcomb (2006) Ann. Phys., 10, 232] small solutions are
allowed, whereas in relaxed MHD only the odd-parity large solution and
even-parity small solution are allowed. A procedure for constructing global
multi-region solutions in cylindrical geometry is presented. Focussing on the
limit where the two interfaces approach each other arbitrarily closely, it is
shown that the singular-limit problem encountered previously [M.J. Hole et al.
(2006) J. Plasma Phys., 77, 1167] in multi-region relaxed MHD is stabilised if
the relaxed-MHD region between the coalescing interfaces is replaced by an
ideal-MHD region. We then present a stable (k, pressure) phase space plot,
which allows us to determine the form a stable pressure and field profile must
take in the region between the interfaces. From this knowledge, we conclude
that there exists a class of single interface plasmas that were found stable by
Kaiser and Uecker [R. Kaiser et al (2004) Q. Jl Mech. Appl. Math., 57, 1], but
are shown to be unstable when the interface is resolved.
