The author studies the bifurcation of vector fields through a saddle-node equilibrium point with an unstable homoclinic orbit. The study is made in the setting of two parameters perturbations of the vector fields \((X_{\mu})_{\mu\in\mathbb{R}^2}\) and in the case that \(X_{(0,0)}\) exhibits an inclination-flip homoclinic orbit associated to the singularity, that is, an equilibrium point where the linearization matrix of the vector field has three real eigenvalues \(\lambda_1,\lambda_2,\lambda_3\) satisfying \[ \lambda_1<\lambda_2=0<\lambda_3. \] The homoclinic orbit is an inclination-flip if: (1) it belongs to \( (W^{cu}(0)\cap W^{cs}(0))\setminus (W^{u}(0)\cap W^{s}(0))\) where \(W^{cu}(0),W^{cs}(0), W^{u}(0), W^{s}(0)\) are respectively the center-unstable, center-stable, unstable and stable manifolds associated to the point \(0\in\mathbb{R}^3\); (2) \(W^{cu}(0)\) and \(W^{cs}(0)\) have a quadratic tangengy along the homoclinic orbit. Let \(F\) be the set of three-dimensional vector fields having an inclination-flip saddle-node homoclinic orbit which is a codimension two submanifold in the space of three-dimensional vector fields. The author introduces two notions concerning the parameters: (a) \(\mu\) is shape hyperbolic relative to a neighborhood \(U\) of the homoclinic orbit if and only if the nonwandering set of the corresponding vector field in \(U\) is either an empty set or a hyperbolic one; (b) \(\mu\) is a shape suspended horseshoe parameter relative to \(U\) if and only if such a nonwandering set is a suspended Smale horseshoe. Under the above conditions, the author proves that if \((X_{\mu})\) is a two parameter family of three-dimensional vector fields transverse to \(F\) at \(\mu =(0,0)\) and if \(U\) is a small neighborhood of the corresponding inclination-flip saddle-node homoclinic orbit, then the set of shape hyperbolic parameters relative to \(U\) has positive Lebesgue density at \((0,0)\) and the set of shape suspended horseshoe parameters relative to \(U\) has positive Lebesgue density at the same parameter value. As a corollary, it is also proved that if \((X_{\mu})\) is a generic two parameter family such that \(X_{(0,0)}\) has a saddle-node singularity, \(p\) transversal homoclinic orbits, and one inclination-flip homoclinic orbit, all of them lying in the interior of the corresponding center manifolds, then, for a small neighborhood \(U\) of these homoclinic orbits, the set of parameters \(\mu\) such that the nonwandering set of \(X_{\mu}\) in \(U\) is either a hyperbolic set conjugated to a subshift of \(p\)-symbols, a hyperbolic set conjugated to a subshift of \((p+2)\)-symbols, or two hyperbolic singularities, has full two-dimensional Lebesgue density at \((0,0)\). In the paper it is also pointed out that there exists some relation between the existence of an inclination-flip homoclinic loop and the presence of geometric Lorenz attractors in the unfolding of the homoclinic orbit. This fact has also been considered by \textit{V. Naudot} [Ergodic Theory Dyn. Syst. 16, No. 5, 1071-1086 (1996; Zbl 0866.58045)] in a similar situation. The viewpoint adopted in the paper and in the proofs of the theorems is that what concerns the prevalence of positive densities to describe the dynamic bifurcations [see \textit{J. Palis} and \textit{F. Takens}, `Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations' (Cambridge University Press 35) (1993; Zbl 0790.58014)].